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Journal of Applied Logic Follow
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ISSN (Print) 1570-8683
Published by Elsevier

[2546 journals] [SJR: 1.079] [H-I: 17]

A logical framework for privacy-preserving social network publication
- Abstract: Publication date: Available online 31 December 2013
  Source:Journal of Applied Logic
  Author(s): Tsan-sheng Hsu , Churn-Jung Liau , Da-Wei Wang
  Social network analysis is an important methodology in sociological research. Although social network data are valuable resources for data analysis, releasing the data to the public may cause an invasion of privacy. In this paper, we consider privacy preservation in the context of publishing social network data. To address privacy concerns, information about a social network can be released in two ways. Either the global structure of the network can be released in an anonymized way; or non-sensitive information about the actors in the network can be accessed via a query-answering process. However, an attacker could re-identify the actors in the network by combining information obtained in these two ways. The resulting privacy risk depends on the amount of detail in the released network structure and expressiveness of the admissible queries. In particular, different sets of admissible queries correspond to different types of attacks. In this paper, we propose a logical framework that can represent different attack models uniformly. Specifically, in the framework, individuals that satisfy the same subset of admissible queries are considered indiscernible by the attacker. By partitioning a social network into equivalence classes (i.e., information granules) based on the indiscernibility relation, we can generalize the privacy criteria developed for tabulated data to social network data. To exemplify the usability of the framework, we consider two instances of the framework, where the sets of admissible queries are the ALCI and ALCQI concept terms respectively; and we exploit social position analysis techniques to compute their indiscernibility relations. We also show how the framework can be extended to deal with the privacy-preserving publication of weighted social network data. The uniformity of the framework provides us with a common ground to compare existing attack models; while its generality could extend the scope of research to meet privacy concerns in the era of social semantic computing.
  
  PubDate: 2014-01-04T04:23:59Z
Empiricism, probability, and knowledge of arithmetic: A preliminary defense
- Abstract: Publication date: Available online 31 December 2013
  Source:Journal of Applied Logic
  Author(s): Sean Walsh
  The topic of this paper is our knowledge of the natural numbers, and in particular, our knowledge of the basic axioms for the natural numbers, namely the Peano axioms. The thesis defended in this paper is that knowledge of these axioms may be gained by recourse to judgements of probability. While considerations of probability have come to the forefront in recent epistemology, it seems safe to say that the thesis defended here is heterodox from the vantage point of traditional philosophy of mathematics. So this paper focuses on providing a preliminary defense of this thesis, in that it focuses on responding to several objections. Some of these objections are from the classical literature, such as Fregeʼs concern about indiscernibility and circularity (§ 2.1), while other are more recent, such as Bakerʼs concern about the unreliability of small samplings in the setting of arithmetic (§ 2.2). Another family of objections suggests that we simply do not have access to probability assignments in the setting of arithmetic, either due to issues related to the ω-rule (§ 3.1) or to the non-computability and non-continuity of probability assignments (§ 3.2). Articulating these objections and the responses to them involves developing some non-trivial results on probability assignments (Appendix A–Appendix C), such as a forcing argument to establish the existence of continuous probability assignments that may be computably approximated (Theorem 4 Appendix B). In the concluding section, two problems for future work are discussed: developing the source of arithmetical confirmation and responding to the probabilistic liar.
  
  PubDate: 2014-01-04T04:23:59Z
Editorial Board
- Abstract: Publication date: December 2013
  Source:Journal of Applied Logic, Volume 11, Issue 4
  
  PubDate: 2013-10-28T11:10:21Z
SLAP: Specification Logic of Actions with Probability
- Abstract: Publication date: Available online 23 October 2013
  Source:Journal of Applied Logic
  Author(s): Gavin Rens , Thomas Meyer , Gerhard Lakemeyer
  A logic for specifying probabilistic transition systems is presented. Our perspective is that of agents performing actions. A procedure for deciding whether sentences in this logic are valid is provided. One of the main contributions of the paper is the formulation of the decision procedure: a tableau system which appeals to solving systems of linear equations. The tableau rules eliminate propositional connectives, then, for all open branches of the tableau tree, systems of linear equations are generated and checked for feasibility. Proofs of soundness, completeness and termination of the decision procedure are provided.
  
  PubDate: 2013-10-24T03:34:35Z
A neural cognitive model of argumentation with application to legal inference and decision making
- Abstract: Publication date: Available online 23 October 2013
  Source:Journal of Applied Logic
  Author(s): Artur S. dʼAvila Garcez , Dov M. Gabbay , Luis C. Lamb
  Formal models of argumentation have been investigated in several areas, from multi-agent systems and artificial intelligence (AI) to decision making, philosophy and law. In artificial intelligence, logic-based models have been the standard for the representation of argumentative reasoning. More recently, the standard logic-based models have been shown equivalent to standard connectionist models. This has created a new line of research where (i) neural networks can be used as a parallel computational model for argumentation and (ii) neural networks can be used to combine argumentation, quantitative reasoning and statistical learning. At the same time, non-standard logic models of argumentation started to emerge. In this paper, we propose a connectionist cognitive model of argumentation that accounts for both standard and non-standard forms of argumentation. The model is shown to be an adequate framework for dealing with standard and non-standard argumentation, including joint-attacks, argument support, ordered attacks, disjunctive attacks, metalevel attacks, self-defeating attacks, argument accrual and uncertainty. We show that the neural cognitive approach offers an adequate way of modelling all of these different aspects of argumentation. We have applied the framework to the modelling of a public prosecution charging decision as part of a real legal decision making case study containing many of the above aspects of argumentation. The results show that the model can be a useful tool in the analysis of legal decision making, including the analysis of what-if questions and the analysis of alternative conclusions. The approach opens up two new perspectives in the short-term: the use of neural networks for computing prevailing arguments efficiently through the propagation in parallel of neuronal activations, and the use of the same networks to evolve the structure of the argumentation network through learning (e.g. to learn the strength of arguments from data).
  
  PubDate: 2013-10-24T03:34:35Z
Modelling Martin Löf Type Theory in Categories
- Abstract: Publication date: Available online 4 September 2013
  Source:Journal of Applied Logic
  Author(s): François Lamarche
  We present a model of Martin-Löf type theory that includes both dependent products and the identity type. It is based on the category of small categories, with cloven Grothendieck bifibrations used to model dependent types. The identity type is modelled by a path functor that seems to have independent interest from the point of view of homotopy theory. We briefly describe this modelʼs strengths and limitations.
  
  PubDate: 2013-09-08T02:05:58Z
Selectional restrictions, types and categories
- Abstract: Publication date: Available online 23 August 2013
  Source:Journal of Applied Logic
  Author(s): Nicholas Asher
  
  PubDate: 2013-08-27T03:32:03Z
Natural language semantics in biproduct dagger categories
- Abstract: Publication date: Available online 23 August 2013
  Source:Journal of Applied Logic
  Author(s): Anne Preller
  Biproduct dagger categories serve as models for natural language. In particular, the biproduct dagger category of finite dimensional vector spaces over the field of real numbers accommodates both the extensional models of predicate calculus and the intensional models of quantum logic. The morphisms representing the extensional meanings of a grammatical string are translated to morphisms representing the intensional meanings such that truth is preserved. Pregroup grammars serve as the tool that transforms a grammatical string into a morphism. The chosen linguistic examples concern negation, relative noun phrases, comprehension and quantifiers.
  
  PubDate: 2013-08-27T03:32:03Z
Infinity and verifiability in Carnapʼs inductive logic
- Abstract: Publication date: Available online 20 August 2013
  Source:Journal of Applied Logic
  Author(s): Ruurik Holm
  Truth of sentences in infinity is discussed in the framework of Rudolf Carnapʼs inductive logic, which uses finite state descriptions and an asymptotic limit approach for defining probabilities in infinity. This means that Carnapʼs approach suits well for a semantics which is based on finite observability. However, a proper link between asymptotic probability and truth in infinity is missing from Carnapʼs treatment. A novel notion of truth in infinity is introduced and referred to as the extended truth. The idea is that the truth of the sentence S is extended by a particular sequence of state descriptions (where the larger one contains all of the smaller ones) iff S is true in each state description of the sequence. The corresponding notion of extended probability is introduced. Some important results are proved for extended truth and extended probability.
  
  PubDate: 2013-08-23T12:31:00Z
The sure thing principle, dilations, and objective probabilities
- Abstract: Publication date: Available online 13 August 2013
  Source:Journal of Applied Logic
  Author(s): Haim Gaifman
  The common theme that unites the four sections is STP, the sure thing principle. But the paper can be divided neatly into two parts. The first, consisting of the first two sections, contains an analysis of STP as it figures in Savageʼs system and proposals of changes to that system. Also possibilities for partially ordered acts are considered. The second, consisting of the last two sections, is about imprecise probabilities, dilations and objective probabilities. Variants of STP are considered but this part is self-contained and can be read separately. The main claim there is that dilations, which can have extremely counterintuitive consequences, can be eliminated by a more careful analysis of the phenomenon. It outlines a proposal of how to do it.
  
  PubDate: 2013-08-15T14:08:31Z
Relational semantics for full linear logic
- Abstract: Publication date: Available online 7 August 2013
  Source:Journal of Applied Logic
  Author(s): Dion Coumans , Mai Gehrke , Lorijn van Rooijen
  Relational semantics, given by Kripke frames, play an essential role in the study of modal and intuitionistic logic. In [4] it is shown that the theory of relational semantics is also available in the more general setting of substructural logic, at least in an algebraic guise. Building on these ideas, in [5] a type of frames is described which generalise Kripke frames and provide semantics for substructural logics in a purely relational form. In this paper we study full linear logic from an algebraic point of view. The main additional hurdle is the exponential. We analyse this operation algebraically and use canonical extensions to obtain relational semantics. Thus, we extend the work in [4,5] and use their approach to obtain relational semantics for full linear logic. Hereby we illustrate the strength of using canonical extension to retrieve relational semantics: it allows a modular and uniform treatment of additional operations and axioms. Traditionally, so-called phase semantics are used as models for (provability in) linear logic [7]. These have the drawback that, contrary to our approach, they do not allow a modular treatment of additional axioms. However, the two approaches are related, as we will explain.
  
  PubDate: 2013-08-11T02:06:43Z
Editorial Board
- Abstract: Publication date: September 2013
  Source:Journal of Applied Logic, Volume 11, Issue 3
  
  PubDate: 2013-08-03T08:06:39Z
Formal Ontologies and Coherent Spaces
- Abstract: Publication date: Available online 25 July 2013
  Source:Journal of Applied Logic
  Author(s): V. Michele Abrusci , Christophe Fouqueré , Marco Romano
  The paper contains a short summary – oriented by a logical point of view – of a joint work on Formal Ontolgies. We shall show how Formal Ontologies correspond to Coherent Spaces, and operations on Formal Ontologies correspond to operations on corresponding Coherent Spaces. So, we are offering a new way to establish the semantics of Formal Ontologies. Surely, we are giving a contribution towards a geometrical treatment of Formal Ontologies (as decidable organizations of digital data).
  
  PubDate: 2013-07-26T02:07:39Z
An epistemic and dynamic approach to abductive reasoning: Abductive problem and abductive solution
- Abstract: Publication date: Available online 25 July 2013
  Source:Journal of Applied Logic
  Author(s): Fernando R. Velázquez-Quesada , Fernando Soler-Toscano , Ángel Nepomuceno-Fernández
  We propose a study of abductive reasoning addressing it as an epistemic process that involves both an agentʼs information and the actions that modify this information. More precisely, we present and discuss definitions of an abductive problem and an abductive solution in terms of an agentʼs information, that is, in terms of knowledge and beliefs. The discussion is then formalised by ‘implementing’ our definitions in a dynamic epistemic logic framework, where the properties of these definitions are studied, an epistemic action that represents the application of an abductive step is introduced, and an illustrative example is provided. A number of the most interesting properties of abductive reasoning (those highlighted by Peirce) are shown to be better modelled within this approach.
  
  PubDate: 2013-07-26T02:07:39Z
Continuity and geometric logic
- Abstract: Publication date: Available online 25 July 2013
  Source:Journal of Applied Logic
  Author(s): Steven Vickers
  This paper is largely a review of known results about various aspects of geometric logic. Following Grothendieckʼs view of toposes as generalized spaces, one can take geometric morphisms as generalized continuous maps. The constructivist constraints of geometric logic guarantee the continuity of maps constructed, and can do so from two different points of view: for maps as point transformers and maps as bundles.
  
  PubDate: 2013-07-26T02:07:39Z
On the a priori and a posteriori assessment of probabilities
- Abstract: Publication date: Available online 11 July 2013
  Source:Journal of Applied Logic
  Author(s): A. Vasudevan
  We argue that in spite of their apparent dissimilarity, the methodologies employed in the a priori and a posteriori assessment of probabilities can both be justified by appeal to a single principle of inductive reasoning, viz., the principle of symmetry. The difference between these two methodologies consists in the way in which information about the single-trial probabilities in a repeatable chance process is extracted from the constraints imposed by this principle. In the case of a posteriori reasoning, these constraints inform the analysis by fixing an a posteriori determinant of the probabilities, whereas, in the case of a priori reasoning, they imply certain claims which then serve as the basis for subsequent probabilistic deductions. In a given context of inquiry, the particular form which a priori or a posteriori reason may take depends, in large part, on the strength of the underlying symmetry assumed: the stronger the symmetry, the more information can be acquired a priori and the less information about the long-run behavior of the process is needed for an a posteriori assessment of the probabilities. In the context of this framework, frequency-based reasoning emerges as a limiting case of a posteriori reasoning, and reasoning about simple games of chance, as a limiting case of a priori reasoning. Between these two extremes, both a priori and a posteriori reasoning can take a variety of intermediate forms.
  
  PubDate: 2013-07-14T03:56:19Z
Abducted by Bayesians?
- Abstract: Publication date: Available online 3 July 2013
  Source:Journal of Applied Logic
  Author(s): Jan-Willem Romeijn
  This paper discusses the role of theoretical notions in making predictions and evaluating statistical models. The core idea of the paper is that such theoretical notions can be spelled out in terms of priors over statistical models, and that such priors can themselves be assigned probabilities. The discussion substantiates the claim that the use of theoretical notions may offer specific empirical advantages. Moreover, I argue that this use of theoretical notions explicates a particular kind of abductive inference. The paper thus contributes to the discussion over Bayesian models of abductive inference.
  
  PubDate: 2013-07-06T03:36:03Z
Combining Probability and Logic: Papers from Progic 2011
- Abstract: Publication date: Available online 1 July 2013
  Source:Journal of Applied Logic
  Author(s): Jeffrey Helzner
  
  PubDate: 2013-07-02T02:09:59Z
Multiple-valued logic mathematical approaches for multi-state system reliability analysis
- Abstract: Publication date: Available online 21 June 2013
  Source:Journal of Applied Logic
  Author(s): Elena Zaitseva , Vitaly Levashenko
  A mathematical description of an examined system such as Multi-State System (MSS) permits the system reliability to be analysed in more detail, because the MSS defines some performance levels (more than only working and failure). The structure function is one of the basic definitions and representations of MSS. But the dimension of the structure function increases critically depending on the number of system components. Therefore, the development of methods for examination and quantification of such a function is an actual problem in MSS reliability analysis. In this paper, a method for the analysis of the MSS structure function of high dimension is proposed. The principal point of this method is the interpretation of the MSS structure function as a Multiple-Valued Logic function. It allows effective and approved mathematical methods of Multiple-Valued Logic to be used for analysis and quantification of the MSS structure function. We propose to use two mathematical approaches of Multiple-Valued Logic for the MSS. One of them is a representation of the MSS structure function by a Multiple-Valued Decision Diagram. It is an effective approach for analysis and estimation of the function of high dimension in Multiple-Valued Logic. The other approach is Logic Differential Calculus. Logic Differential Calculus is a useful approach for analysis of the MSS state changes.
  
  PubDate: 2013-06-24T02:07:07Z
Preservation of Craig interpolation by the product of matrix logics
- Abstract: Publication date: Available online 18 June 2013
  Source:Journal of Applied Logic
  Author(s): C. Sernadas , J. Rasga , A. Sernadas
  The product of matrix logics, possibly with additional interaction axioms, is shown to preserve a slightly relaxed notion of Craig interpolation. The result is established symbolically, capitalizing on the complete axiomatization of the product of matrix logics provided by their meet-combination. Along the way preservation of the metatheorem of deduction is also proved. The computation of the interpolant in the resulting logic is proved to be polynomially reducible to the computation of the interpolants in the two given logics. Illustrations are provided for classical, intuitionistic and modal propositional logics.
  
  PubDate: 2013-06-20T02:07:17Z
A sequent calculus for a logic of contingencies
- Abstract: Publication date: Available online 4 June 2013
  Source:Journal of Applied Logic
  Author(s): Michael Tiomkin
  We introduce a sequent calculus that is sound and complete with respect to propositional contingencies, i.e., formulas which are neither provable nor refutable. Like many other sequent and natural deduction proof systems, this calculus possesses the subformula property and has a simple proof search mechanism.
  
  PubDate: 2013-06-08T02:07:04Z
A general first-order solution to the ramification problem with cycles
- Abstract: Publication date: Available online 4 June 2013
  Source:Journal of Applied Logic
  Author(s): Hannes Strass , Michael Thielscher
  We provide a solution to the ramification problem that integrates findings of different axiomatic approaches to ramification from the last ten to fifteen years. For the first time, we present a solution that: (1) is independent of a particular time structure, (2) is formulated in classical first-order logic, (3) treats cycles – a notoriously difficult aspect – properly, and (4) is assessed against a state-transition semantics via a formal correctness proof. This is achieved as follows: We introduce indirect effect laws that enable us to specify ramifications that are triggered by activation of a formula rather than just an atomic effect. We characterise the intended models of these indirect effect laws by a state-transition semantics. Afterwards, we show how to compile a class of indirect effect laws into first-order effect axioms that then solve the ramification and frame problems. We finally prove the resulting effect axioms sound and complete with respect to the semantics defined earlier.
  
  PubDate: 2013-06-08T02:07:04Z
Sound Approximate Reasoning about Saturated Conditional Probabilistic Independence under Controlled Uncertainty
- Abstract: Publication date: Available online 3 June 2013
  Source:Journal of Applied Logic
  Author(s): Sebastian Link
  Knowledge about complex events is usually incomplete in practice. We distinguish between random variables that can be assigned a designated marker to model missing data values, and certain random variables to which the designated marker cannot be assigned. The ability to specify an arbitrary set of certain random variables provides an effective mechanism to control the uncertainty in form of missing data values. A finite axiomatization for the implication problem of saturated conditional independence statements is established under controlled uncertainty, relative to discrete probability measures. The completeness proof utilizes special probability models where two assignments have probability one half. The special probability models enable us to establish an equivalence between the implication problem and that of a propositional fragment in Cadoli and Schaerfʼs S -3 logic. Here, the propositional variables in S correspond to the random variables specified to be certain. The duality leads to an almost linear time algorithm to decide implication. It is shown that this duality cannot be extended to cover general conditional independence statements. All results subsume classical reasoning about saturated conditional independence statements as the idealized special case where every random variable is certain. Under controlled uncertainty, certain random variables allow us to soundly approximate classical reasoning about saturated conditional independence statements.
  
  PubDate: 2013-06-04T03:38:01Z
The expressibility of fragments of Hybrid Graph Logic on finite digraphs
- Abstract: Publication date: Available online 24 May 2013
  Source:Journal of Applied Logic
  Author(s): James Gate , Iain A. Stewart
  Hybrid Graph Logic is a logic designed for reasoning about graphs and is built from a basic modal logic, augmented with the use of nominals and a facility to verify the existence of paths in graphs. We study the finite model theory of Hybrid Graph Logic. In particular, we develop pebble games for Hybrid Graph Logic and use these games to exhibit strict infinite hierarchies involving fragments of Hybrid Graph Logic when the logic is used to define problems involving finite digraphs. These fragments are parameterized by the quantifier-rank of formulae along with the numbers of propositional symbols and nominals that are available. We ascertain exactly the relative definability of these parameterized fragments of the logic.
  
  PubDate: 2013-05-27T02:07:28Z
Ordered domain algebras
- Abstract: Publication date: Available online 2 May 2013
  Source:Journal of Applied Logic
  Author(s): Robin Hirsch , Szabolcs Mikulás
  We give a finite axiomatisation to representable ordered domain algebras and show that finite algebras are representable on finite bases.
  
  PubDate: 2013-05-03T02:08:16Z
A model of type theory in simplicial sets
- Abstract: Publication date: Available online 24 April 2013
  Source:Journal of Applied Logic
  Author(s): T. Streicher
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  PubDate: 2013-04-29T02:07:39Z
Editorial Board
- Abstract: Publication date: June 2013
  Source:Journal of Applied Logic, Volume 11, Issue 2
  
  PubDate: 2013-04-25T02:07:34Z
Skew Lattices and Binary Operations on Functions
- Abstract: Available online 30 March 2013
  Publication year: 2013
  Source:Journal of Applied Logic
  
  A recent study of the override and update operations defined on sets of partial functions placed both operations within the algebraic context of a certain variety of algebras. We show the latter to be term equivalent to the variety of right-handed skew Boolean algebras. Both operations are then studied within the broader context of skew lattices with an eye towards achieving greater insight into their joint algebraic behavior. A decision procedure is given to determine whether an equation in both operations holds for all sets of partial functions.
  
  PubDate: 2013-04-01T02:09:36Z
Simulative belief logic
- Abstract: Available online 21 March 2013
  Publication year: 2013
  Source:Journal of Applied Logic
  
  The ability of ascribing beliefs to others is crucial for human beings to explain and understand each other. Belief ascription has been studied intensively in philosophy and cognitive science. In this paper, we propose a formal framework for belief ascription by simulation. An agent first acquires information about another agentʼs beliefs by communication. She then inputs the information into her own belief system to generate more beliefs, which she will ascribe to the other agent. In this way, the agent uses her own as a model of others. We present a modal belief logic, which contains private announcement operators for agentsʼ communication, and simulative belief operators for beliefs ascribed to others. We give a complete axiomatic system for the logic.
  
  PubDate: 2013-03-24T03:07:29Z
Modal definability of first-order formulas with free variables and query answering
- Abstract: Available online 20 March 2013
  Publication year: 2013
  Source:Journal of Applied Logic
  
  We present an algorithmically efficient criterion of modal definability for first-order existential conjunctive formulas with several free variables. Then we apply it to establish modal definability of some family of first-order ∀∃-formulas. Finally, we use our definability results to show that, in any expressive description logic, the problem of answering modally definable conjunctive queries is polynomially reducible to the problem of knowledge base consistency.
  
  PubDate: 2013-03-24T03:07:29Z
A QBF-based formalization of abstract argumentation semantics
- Abstract: Available online 21 March 2013
  Publication year: 2013
  Source:Journal of Applied Logic
  
  We introduce a unified logical theory, based on signed theories and Quantified Boolean Formulas (QBFs) that can serve as the basis for representing and computing various argumentation-based decision problems. It is shown that within our framework we are able to model, in a simple and modular way, a wide range of semantics for abstract argumentation theory. This includes complete, grounded, preferred, stable, semi-stable, stage, ideal and eager semantics. Furthermore, our approach is purely logical, making for instance decision problems like skeptical and credulous acceptance of arguments simply a matter of entailment and satisfiability checking. The latter may be verified by off-the-shelf QBF-solvers.
  
  PubDate: 2013-03-24T03:07:29Z
An observation on Carnapʼs Continuum and Stochastic Independencies
- Abstract: Available online 18 March 2013
  Publication year: 2013
  Source:Journal of Applied Logic
  
  We characterize those identities and independencies which hold for all probability functions on a unary language satisfying the Principle of Atom Exchangeability. We then show that if this is strengthen to the requirement that Johnsonʼs Sufficientness Principle holds, thus giving Carnapʼs Continuum of inductive methods for languages with at least two predicates, then new and somewhat inexplicable identities and independencies emerge, the latter even in the case of Carnapʼs Continuum for the language with just a single predicate.
  
  PubDate: 2013-03-20T03:07:19Z
From Bayesian epistemology to inductive logic
- Abstract: Available online 18 March 2013
  Publication year: 2013
  Source:Journal of Applied Logic
  
  Inductive logic admits a variety of semantics [7, Part 1]. This paper develops semantics based on the norms of Bayesian epistemology [16, Chapter7]. §1 introduces the semantics and then, in $ 2, the paper explores methods for drawing inferences in the resulting logic and compares the methods of this paper with the methods of Barnett and Paris [2]. §3 then evaluates this Bayesian inductive logic in the light of four traditional critiques of inductive logic, arguing (i) that it is language independent in a key sense, (ii) that it admits connections with the Principle of Indifference but these connections do not lead to paradox, (iii) that it can capture the phenomenon of learning from experience, and (iv) that while the logic advocates scepticism with regard to some universal hypotheses, such scepticism is not problematic from the point of view of scientific theorising.
  
  PubDate: 2013-03-20T03:07:19Z
Confirmation as partial entailment: A representation theorem in inductive logic
- Abstract: Available online 18 March 2013
  Publication year: 2013
  Source:Journal of Applied Logic
  
  The most prominent research program in inductive logic – here just labelled The Program, for simplicity – relies on probability theory as its main building block and aims at a proper generalization of deductive-logical relations by a theory of partial entailment. We prove a representation theorem by which a class of ordinally equivalent measures of inductive support or confirmation is singled out as providing a uniquely coherent way to work out these two major sources of inspiration of The Program.
  
  PubDate: 2013-03-20T03:07:19Z
Probabilities on Sentences in an Expressive Logic
- Abstract: Available online 18 March 2013
  Publication year: 2013
  Source:Journal of Applied Logic
  
  Automated reasoning about uncertain knowledge has many applications. One difficulty when developing such systems is the lack of a completely satisfactory integration of logic and probability. We address this problem directly. Expressive languages like higher-order logic are ideally suited for representing and reasoning about structured knowledge. Uncertain knowledge can be modeled by using graded probabilities rather than binary truth-values. The main technical problem studied in this paper is the following: Given a set of sentences, each having some probability of being true, what probability should be ascribed to other (query) sentences? A natural wish-list, among others, is that the probability distribution (i) is consistent with the knowledge base, (ii) allows for a consistent inference procedure and in particular (iii) reduces to deductive logic in the limit of probabilities being 0 and 1, (iv) allows (Bayesian) inductive reasoning and (v) learning in the limit and in particular (vi) allows confirmation of universally quantified hypotheses/sentences. We translate this wish-list into technical requirements for a prior probability and show that probabilities satisfying all our criteria exist. We also give explicit constructions and several general characterizations of probabilities that satisfy some or all of the criteria and various (counter) examples. We also derive necessary and sufficient conditions for extending beliefs about finitely many sentences to suitable probabilities over all sentences, and in particular least dogmatic or least biased ones. We conclude with a brief outlook on how the developed theory might be used and approximated in autonomous reasoning agents. Our theory is a step towards a globally consistent and empirically satisfactory unification of probability and logic.
  
  PubDate: 2013-03-20T03:07:19Z
Ultralarge lotteries: Analyzing the Lottery Paradox using non-standard analysis
- Abstract: Available online 15 March 2013
  Publication year: 2013
  Source:Journal of Applied Logic
  
  A popular way to relate probabilistic information to binary rational beliefs is the Lockean Thesis, which is usually formalized in terms of thresholds. This approach seems far from satisfactory: the value of the thresholds is not well-specified and the Lottery Paradox shows that the model violates the Conjunction Principle. We argue that the Lottery Paradox is a symptom of a more fundamental and general problem, shared by all threshold-models that attempt to put an exact border on something that is intrinsically vague. We propose application of the language of relative analysis—a type of non-standard analysis—to formulate a new model for rational belief, called Stratified Belief. This contextualist model seems well-suited to deal with a concept of beliefs based on probabilities ‘sufficiently close to unity’ and satisfies a moderately weakened form of the Conjunction Principle. We also propose an adaptation of the model that is able to deal with beliefs that are less firm than ‘almost certainty’. The adapted version is also of interest for the epistemicist account of vagueness.
  
  PubDate: 2013-03-16T03:06:55Z
Representation of interlaced trilattices
- Abstract: Available online 14 March 2013
  Publication year: 2013
  Source:Journal of Applied Logic
  
  Trilattices are algebraic structures introduced ten years ago into logic with the aim to provide a uniform framework for the notions of constructive truth and constructive falsity. In more recent years, trilattices have been used to introduce a number of many-valued systems that generalize the Belnap-Dunn logic of first-degree entailment, proposed as logics of how several computers connected together in a network should think in order to deal with incomplete and possibly contradictory information. The aim of the present work is to develop a first purely algebraic study of trilattices, focusing in particular on the problem of representing certain subclasses of trilattices as special products of bilattices. This approach allows to extend the known representation results for interlaced bilattices to the setting of trilattices and to reduce many algebraic problems concerning these new structures to the better-known framework of lattice theory.
  
  PubDate: 2013-03-16T03:06:55Z
A note on orthogonality of subspaces in Euclidean geometry
- Abstract: Available online 1 March 2013
  Publication year: 2013
  Source:Journal of Applied Logic
  
  We show that Euclidean geometry in suitably high dimension can be expressed as a theory of orthogonality of subspaces with fixed dimensions and fixed dimension of their meet.
  
  PubDate: 2013-03-04T03:08:32Z
Two adaptive logics of norm-propositions
- Abstract: Available online 9 February 2013
  Publication year: 2013
  Source:Journal of Applied Logic
  
  We present two defeasible logics of norm-propositions (statements about norms) that (i) consistently allow for the possibility of normative gaps and normative conflicts, and (ii) map each premise set to a sufficiently rich consequence set. In order to meet (i), we define the logic LNP, a conflict- and gap-tolerant logic of norm-propositions capable of formalizing both normative conflicts and normative gaps within the object language. Next, we strengthen LNP within the adaptive logic framework for non-monotonic reasoning in order to meet (ii). This results in the adaptive logics LNP r and LNP m , which interpret a given set of premises in such a way that normative conflicts and normative gaps are avoided ‘whenever possible’. LNP r and LNP m are equipped with a preferential semantics and a dynamic proof theory.
  
  PubDate: 2013-02-12T01:35:09Z
Editorial Board
- Abstract: March 2013
  Publication year: 2013
  Source:Journal of Applied Logic, Volume 11, Issue 1
  
  PubDate: 2013-01-23T09:13:25Z
Future determination of entities in Talmudic public announcement logic
- Abstract: Available online 12 June 2012
  Publication year: 2012
  Source:Journal of Applied Logic
  
  Ordinary dynamic action logics deal with states and actions upon states. The actions can be deterministic or non-deterministic, but it is always assumed that the possible results of the actions are clear cut. Talmudic logic deals with actions (usually legally meaningful actions which can change the legal status of an entity) which depend on the future and therefore may be not clear cut at the present and need future clarifications. The clarification is modelled by public announcement which comes at a later time after the action has taken place. The model is further complicated by the need to know what is the status of formulas at a time before the results of the action is clarified, as we do not know at which state we are in. Talmudic logic treats such states much like the quantum superposition of states and when clarification is available we get a collapse onto a pure state. The Talmudic lack of clarity of actions arises from applying an action to entities defined using the future, like the statement of a dying man on his death bed: Let the man who will win the jackpot in the lottery next week be the sole heir in my will now We need to wait a week for the situation to clarify. There is also the problem of legal backwards causality, as this man, if indeed he exists, unaware of his possible good fortune, may have himself meanwhile donated all his property to a charity. Does his donation include this unknown inheritance' This paper will offer a model and a logic which can represent faithfully the Talmudic reasoning in these matters. We shall also see that we get new types of public announcement logics and (quantum-like) action logics. Ordinary public announcement logic deletes possible worlds after an announcements. Talmudic public announcement logic deletes accessibility links after an announcement. Technically these two approaches are similar but not equivalent.
  
  PubDate: 2012-12-18T09:16:16Z
Denotation of contextual modal type theory (CMTT): Syntax and meta-programming
- Abstract: Available online 15 July 2012
  Publication year: 2012
  Source:Journal of Applied Logic
  
  The modal logic S4 can be used via a Curry–Howard style correspondence to obtain a λ-calculus. Modal (boxed) types are intuitively interpreted as ‘closed syntax of the calculus’. This λ-calculus is called modal type theory—this is the basic case of a more general contextual modal type theory, or CMTT. CMTT has never been given a denotational semantics in which modal types are given denotation as closed syntax. We show how this can indeed be done, with a twist. We also use the denotation to prove some properties of the system.
  
  PubDate: 2012-12-18T09:16:16Z
Deductive temporal reasoning with constraints
- Abstract: Available online 14 July 2012
  Publication year: 2012
  Source:Journal of Applied Logic
  
  When modelling realistic systems, physical constraints on the resources available are often required. For example, we might say that at most N processes can access a particular resource at any moment, exactly M participants are needed for an agreement, or an agent can be in exactly one mode at any moment. Such situations are concisely modelled where literals are constrained such that at most N, or exactly M, can hold at any moment in time. In this paper we consider a logic which is a combination of standard propositional linear time temporal logic with cardinality constraints restricting the numbers of literals that can be satisfied at any moment in time. We present the logic and show how to represent a number of case studies using this logic. We propose a tableau-like algorithm for checking the satisfiability of formulae in this logic, provide details of a prototype implementation and present experimental results using the prover.
  
  PubDate: 2012-12-18T09:16:16Z
A logic of non-monotonic interactions
- Abstract: Available online 28 September 2012
  Publication year: 2012
  Source:Journal of Applied Logic
  
  In this paper, which is part of the Zsyntax project outlined in Boniolo et al. (2010) [2], we provide a proof-theoretical setting for the study of context-sensitive interactions by means of a non-monotonic conjunction operator. The resulting system is a non-associative variant of MLL pol (the multiplicative polarised fragment of Linear Logic) in which the monotonicity of interactions, depending on the context, is governed by specific devices called control sets. Following the spirit of Linear Logic, the ordinary sequent calculus presentation is also framed into a theory of proof-nets and the set of sequential proofs is shown to be sound and complete with respect to the class of corresponding proof-nets. Some possible biochemical applications are also discussed.
  
  PubDate: 2012-12-18T09:16:16Z
Reactive Kripke models and contrary to duty obligations. Part A: Semantics
- Abstract: Available online 15 September 2012
  Publication year: 2012
  Source:Journal of Applied Logic
  
  This paper introduces a new method for modelling contrary to duty obligations (CTD). Given a contrary to duty obligation structure CTDs presented in English, there is the problem of offering a logical system in which it can be coherently formalised. There are several formal systems in the literature attempting to do so, such as SDL (Standard Deontic Logic), various dyadic operators and other kinds of formalised normative systems. The difficulties encountered by such systems is that they end up with counter intuitive results for some CTD linguistic structures, referred to as paradoxes (for the offered formalising logic). We use reactive Kripke models as the semantics and a reactive extension of SDL, with one additional reactive modality as syntax for such CTD. Reactive Kripke models change their accessibility relation as we move from node to node during the semantic evaluation process. This change is made to correspond to the change implicit in the intuitive meaning of the contrary to duty obligations. The reactive Kripke semantics is stronger semantics than ordinary Kripke models and therefore allows for more fine tuning of our modelling process.
  
  PubDate: 2012-12-18T09:16:16Z
Selected papers from the 6th International Conference on Soft Computing Models in Industrial and Environmental Applications
- Abstract: December 2012
  Publication year: 2012
  Source:Journal of Applied Logic, Volume 10, Issue 4
  
  PubDate: 2012-12-18T09:16:16Z
An intelligent task analysis approach for special education based on MIRA
- Abstract: Available online 14 December 2012
  Publication year: 2012
  Source:Journal of Applied Logic
  
  This paper describes a novel approach for generating a logical sequence of tasks in the task analysis process of special education. This approach is based on the formalism MIRA (Mīmāṁsā Inspired Representation of Actions), which has the feature of expressing an action as reason, instruction and goal. MIRA also prescribes a set of deduction rules, which helps in the reasoning process of actions. These features are incorporated in this approach and a software tool, namely MIRATaskGen is designed, which facilitates the task analysis process of special education. The software receives various action related inputs along with the start and finish stages and generates a sequence of tasks from the start to finish. This tool also informs the user, whether the desired goal can be achieved. If the desired goal cannot be achieved, then the sequence of actions from the start to a point of discontinuity is detected.
  
  PubDate: 2012-12-18T09:16:16Z
LEO-II and Satallax on the Sledgehammer test bench
- Abstract: Available online 13 December 2012
  Publication year: 2012
  Source:Journal of Applied Logic
  
  Sledgehammer is a tool that harnesses external first-order automatic theorem provers (ATPs) to discharge interactive proof obligations arising in Isabelle/HOL. We extended it with LEO-II and Satallax, the two most prominent higher-order ATPs, improving its performance on higher-order problems. To explore their usefulness, these ATPs are measured against first-order ATPs and built-in Isabelle tactics on a variety of benchmarks from Isabelle and the TPTP library. Sledgehammer provides an ideal test bench for individual features of LEO-II and Satallax, revealing areas for improvements.
  
  PubDate: 2012-12-18T09:16:16Z
Editorial Board
- Abstract: December 2012
  Publication year: 2012
  Source:Journal of Applied Logic, Volume 10, Issue 4
  
  PubDate: 2012-12-18T09:16:16Z