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  Subjects -> PHILOSOPHY (Total: 762 journals)
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Studia Logica
Journal Prestige (SJR): 0.353
Citation Impact (citeScore): 1
Number of Followers: 3  
 
  Hybrid Journal Hybrid journal (It can contain Open Access articles)
ISSN (Print) 1572-8730 - ISSN (Online) 0039-3215
Published by Springer-Verlag Homepage  [2468 journals]
  • Dynamic Logics of Diffusion and Link Changes on Social Networks

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      Abstract: Abstract This paper introduces a comprehensive logical framework to reason about threshold-driven diffusion and threshold-driven link change in social networks. It considers both monotonic dynamics, where agents can only adopt new features and create new connections, and non-monotonic dynamics, where agents may also abandon features or cut ties. Three types of operators are combined: one capturing diffusion only, one capturing link change only, and one capturing both at the same time. We first characterise the models on which diffusion of a unique feature and link change stabilise, whilst discussing salient properties of stable models with multiple spreading features. Second, we show that our operators (and any combination of them) are irreplaceable, in the sense that the sequences of model updates expressed by a combination of operators cannot always be expressed using any other operators. Finally, we analyse classes of models on which some operators can be replaced.
      PubDate: 2024-07-17
       
  • Probabilistic Semantics and Calculi for Multi-valued and Paraconsistent
           Logics

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      Abstract: Abstract We show how to obtain a probabilistic semantics and calculus for a logic presented by a valuation specification. By identifying general forms of valuation constraints we are able to accommodate a wide class of propositional based logics encompassing multi-valued logics like Łukasiewicz 3-valued logic and the Belnap–Dunn four-valued logic as well as paraconsistent logics like \({\textsf{mbC}}\) and \({\textsf{LFI1}}\) . The probabilistic calculus is automatically generated from the valuation specification. Although not having explicit probability constructors in the language, the rules of the calculus reflect the valuation constraints in a probabilistic way. Indeed the probability of the premises of each rule coincides with the probability of the conclusions. Moreover, a failed exhaustive attempt of proving a formula in this calculus means non-derivability. Nevertheless when the non-derived formula is consistent then it is possible to extract a satisfying valuation from the failed exhaustive attempt. Soundness and completeness of the calculi are established with respect to the probabilistic semantics consisting of probability spaces also induced by the valuation specification. Furthermore we prove the equivalence between the probabilistic and the valuation semantics.
      PubDate: 2024-07-15
       
  • Free Constructions in Hoops via $$\ell $$ -Groups

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      Abstract: Abstract Lattice-ordered abelian groups, or abelian \(\ell \) -groups in what follows, are categorically equivalent to two classes of 0-bounded hoops that are relevant in the realm of the equivalent algebraic semantics of many-valued logics: liftings of cancellative hoops and perfect MV-algebras. The former generate the variety of product algebras, and the latter the subvariety of MV-algebras generated by perfect MV-algebras, that we shall call \(\textsf{DLMV}\) . In this work we focus on these two varieties and their relation to the structures obtained by forgetting the falsum constant 0, i.e., product hoops and DLW-hoops. As main results, we first show a characterization of the free algebras in these two varieties as particular weak Boolean products; then, we show a construction that freely generates a product algebra from a product hoop and a DLMV-algebra from a DLW-hoop. In other words, we exhibit the free functor from the two algebraic categories of hoops to the corresponding categories of 0-bounded algebras. Finally, we use the results obtained to study projective algebras and unification problems in the two varieties (and the corresponding logics); both varieties are shown to have (strong) unitary unification type, and as a consequence they are structurally and universally complete.
      PubDate: 2024-07-15
       
  • More Limits of Abductivism About Logic

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      Abstract: Abstract Logical abductivism is the method which purports to use Inference to the Best Explantion (IBE) to determine the best logical theory. The present essay argues that this is not the case, since the method fails to meet the criteria requisite for the fruitful application of IBE. This occurs due to an intrinsic difficulty in choosing the appropriate evidence and theoretical virtues which guide theory revision in logic: one’s previous conception of logic influences both these choices. Logical abductivism fails, moreover, to select the best logical theory, exactly because a lack of agreement on theory and virtues for Logic. Rather than direct comparison between two options, a more suitable approach to theory revision in logic is piecemeal, because this method neither assumes nor needs a neutral ground from which to start revising theories.
      PubDate: 2024-07-15
       
  • A Version of Predicate Logic with Two Variables That has an Incompleteness
           Property

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      Abstract: Abstract In this paper, we consider predicate logic with two individual variables and general assignment models (where the set of assignments of the variables into a model is allowed to be an arbitrary subset of the usual one). We prove that there is a statement such that no general assignment model in which it is true can be finitely axiomatized. We do this by showing that the free relativized cylindric algebras of dimension two are not atomic.
      PubDate: 2024-07-15
       
  • Constructive Validity of a Generalized Kreisel–Putnam Rule

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      Abstract: Abstract In this paper, we propose a computational interpretation of the generalized Kreisel–Putnam rule, also known as the generalized Harrop rule or simply the Split rule, in the style of BHK semantics. We will achieve this by exploiting the Curry–Howard correspondence between formulas and types. First, we inspect the inferential behavior of the Split rule in the setting of a natural deduction system for intuitionistic propositional logic. This will guide our process of formulating an appropriate program that would capture the corresponding computational content of the typed Split rule. Our investigation can also be reframed as an effort to answer the following question: is the Split rule constructively valid in the sense of BHK semantics' Our answer is positive for the Split rule as well as for its newly proposed general version called the S rule.
      PubDate: 2024-07-15
       
  • Decidability of Inquisitive Modal Logic via Filtrations

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      Abstract: Abstract Inquisitive logic is an extension of classical logic which can express questions. To enable this expressiveness, a possible world semantics is used. So, it is natural to combine inquisitive and modal logic, thus obtaining the inquisitive modal logic \(\textrm{InqML}\) . This paper contributes to the model theory of \(\textrm{InqML}\) . We show that the filtration technique can be adapted to the inquisitive logic semantics. Using filtrations, we prove that \(\textrm{InqML}\) has the finite model property, i.e., every satisfiable formula is satisfiable in a finite model. As a consequence, we obtain that \(\textrm{InqML}\) is decidable. Finally, we study filtrations over particular model classes and we prove that some extensions of \(\textrm{InqML}\) are also decidable.
      PubDate: 2024-07-15
       
  • A New Game Theoretic Semantics (GTS-2) for Weak Kleene Logics

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      Abstract: Abstract Hintikka’s game theoretical approach to semantics has been successfully applied also to some non-classical logics. A recent example is Başkent (A game theoretical semantics for logics of nonsense, 2020. arXiv:2009.10878), where a game theoretical semantics based on three players and the notion of dominant winning strategy is devised to fit both Bochvar and Halldén’s logics of nonsense, which represent two basic systems of the family of weak Kleene logics. In this paper, we present and discuss a new game theoretic semantics for Bochvar and Halldén’s logics, GTS-2, and show how it generalizes to a broader family of logics of variable inclusions.
      PubDate: 2024-07-01
       
  • The Sum Relation as a Primitive Concept of Mereology

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      Abstract: Abstract Mereology in its formal guise is usually couched in a language whose signature contains only one primitive binary predicate symbol representing the part of relation, either the proper or improper one. In this paper, we put forward an approach to mereology that uses mereological sum as its primitive notion, and we demonstrate that it is definitionally equivalent to the standard parthood-based theory of mereological structures.
      PubDate: 2024-07-01
       
  • Oiva Ketonen, Investigations into the Predicate Calculus, vol. 3 of Logic
           PhDs, Sara Negri, and Jan von Plato, (eds.), College Publications, 2022,
           pp. 130+vii; ISBN 978-1-84890-407-1

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      PubDate: 2024-06-25
       
  • Enriched Quantales Arising from Complete Orthomodular Lattices

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      Abstract: Abstract This paper connects complete orthomodular lattices to two enriched quantale structures. Complete orthomodular lattices emphasize a static perspective of a quantum system, helping us reason about testable properties of a quantum system. Quantales offer a dynamic perspective, helping us reason about the structure of quantum actions. We enrich quantales with an orthocomplementation-inducing operator, and call these structures orthomodular dynamic algebras. One type of orthomodular dynamic algebra distinguishes the joins of any two different sets of atoms, while the other distinguishes elements by the collective behavior of the atoms below it. We show that both orthomodular dynamic algebras are unital, and the unit is the top element of an induced orthomodular lattice. We provide a categorical equivalence between both orthomodular dynamic algebras and complete orthomodular lattices with isomorphisms, and we show that this equivalence is preserved when augmenting the orthomodular dynamic algebras with an involution. These equivalences help clarify the relationship between static and dynamic quantum structures.
      PubDate: 2024-06-06
       
  • Higher-Level Paradoxes and Substructural Solutions

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      Abstract: Abstract There have been recent arguments against the idea that substructural solutions are uniform. The claim is that even if the substructuralist solves the common semantic paradoxes uniformly by targeting Cut or Contraction, with additional machinery, we can construct higher-level paradoxes (e.g., a higher-level Liar, a higher-level Curry, and a meta-validity Curry). These higher-level paradoxes do not use metainferential Cut or Contraction, but rather, higher-level Cuts and higher-level Contractions. These kinds of paradoxes suggest that targeting Cut or Contraction is not enough for solving semantic paradoxes; the substructuralist must target Cut of every level or Contraction of every level to solve the paradoxes. Hence, the substructuralists do not provide as uniform of a solution as they hoped they did. In response, we argue that the substructuralists need not admit these additional machineries. In fact, they are redundant in light of the validity predicate (i.e., there is no gain in terms of expressive power). The validity predicate is powerful enough to creep these paradoxes in the object level. The substructuralist does not need to ascend to metainferences to construct higher-level paradoxes. Moreover, there is a reading available to the substructuralist such that all the higher-level structural rules would collapse to instances of the object-level structural rules (e.g., meta \(_n\) Cut and meta \(_n\) Contraction would become instances of Cut and Contraction). We then address Barrio et al.’s worry that the validity predicate has its shortcomings; the substructuralist cannot internalize some of its metarules. We claim that the validity of metarules can be internalized without the need to strengthen the validity predicate. However, a problem raised by Barrio et al. is still present—the problem of internalizing unwanted instances of Cut in Cut-free approaches. We argue that this internalization problem is not unique to the validity predicate; the same problem is present with other problematic predicates, such as the truth predicate and the provability predicate.
      PubDate: 2024-06-06
       
  • Decidability of Lattice Equations

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      Abstract: Abstract We provide an alternative proof of the decidability of the equational theory of lattices. The proof presented here is quite short and elementary.
      PubDate: 2024-06-01
       
  • Unary Interpretability Logics for Sublogics of the Interpretability Logic
           $$\textbf{IL}$$

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      Abstract: Abstract De Rijke introduced a unary interpretability logic \(\textbf{il}\) , and proved that \(\textbf{il}\) is the unary counterpart of the binary interpretability logic \(\textbf{IL}\) . In this paper, we find the unary counterparts of the sublogics of \(\textbf{IL}\) .
      PubDate: 2024-06-01
       
  • Semisimplicity and Congruence 3-Permutabilty for Quasivarieties with
           Equationally Definable Principal Congruences

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      Abstract: Abstract We show that the properties of [relative] semisimplicity and congruence 3-permutability of a [quasi]variety with equationally definable [relative] principal congruences (EDP[R]C) can be characterized syntactically. We prove that a quasivariety with EDPRC is relatively semisimple if and only if it satisfies a finite set of quasi-identities that is effectively constructible from any conjunction of equations defining relative principal congruences in the quasivariety. This in turn allows us to obtain an ‘axiomatization’ of relatively filtral quasivarieties. We also show that a variety is 3-permutable and has EDPC if and only if there is a single pair of quaternary terms satisfying two simple equations, and whose equality defines principal congruences in the variety. Finally, we combine both results to obtain a neat characterization of semisimple, 3-permutable varieties with EDPC, which is applied to solve a problem posed by Blok and Pigozzi in the third paper of their series on varieties with EDPC.
      PubDate: 2024-06-01
       
  • Intuitionistic Public Announcement Logic with Distributed Knowledge

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      Abstract: Abstract We develop intuitionistic public announcement logic over intuitionistic \({\textbf{K}}\) , \({{\textbf{K}}}{{\textbf{T}}}\) , \({{\textbf{K}}}{{\textbf{4}}}\) , and \({{\textbf{S}}}{{\textbf{4}}}\) with distributed knowledge. We reveal that a recursion axiom for the distributed knowledge is not valid for a frame class discussed in [12] but valid for the restricted frame class introduced in [20, 26]. The semantic completeness of the static logics for this restricted frame class is established via the concept of pseudo-model.
      PubDate: 2024-06-01
       
  • $$\varvec{Brings~It~About~That}$$ Operators Decomposed with Relating
           Semantics

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      Abstract: Abstract In the paper we examine the problem of logical systems that are extensions of Classical Propositional Logic with new, intensional connectives of agency: monadic and dyadic bringing it about that. These systems are usually studied within the neighbourhood semantics. Here we propose a different strategy. We study all of the accepted laws and rules of logic of agency and define a translation of the agency operators into connectives interpreted in relating semantics. After this translation we can make a reduction to more basic semantic properties that are required by the particular groups of laws and axioms. Finally, we define proper semantic structures and prove that they are complete with respect to all possible logical systems determined by the combinations of the axioms and rules.
      PubDate: 2024-06-01
       
  • From Belnap-Dunn Four-Valued Logic to Six-Valued Logics of Evidence and
           Truth

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      Abstract: Abstract The main aim of this paper is to introduce the logics of evidence and truth \(LET_{K}^+\) and \(LET_{F}^+\) together with sound, complete, and decidable six-valued deterministic semantics for them. These logics extend the logics \(LET_{K}\) and \(LET_{F}^-\) with rules of propagation of classicality, which are inferences that express how the classicality operator \({\circ }\) is transmitted from less complex to more complex sentences, and vice-versa. The six-valued semantics here proposed extends the 4 values of Belnap-Dunn logic with 2 more values that intend to represent (positive and negative) reliable information. A six-valued non-deterministic semantics for \(LET_{K}\) is obtained by means of Nmatrices based on swap structures, and the six-valued semantics for \(LET_{K}^+\) is then obtained by imposing restrictions on the semantics of \(LET_{K}\) . These restrictions correspond exactly to the rules of propagation of classicality that extend \(LET_{K}\) . The logic \(LET_{F}^+\) is obtained as the implication-free fragment of \(LET_{K}^+\) . We also show that the 6 values of \(LET_{K}^+\) and \(LET_{F}^+\) define a lattice structure that extends the lattice L4 defined by the Belnap-Dunn four-valued logic with the 2 additional values mentioned above, intuitively interpreted as positive and negative reliable information. Finally, we also show that \(LET_{K}^+\) is Blok-Pigozzi algebraizable and that its implication-free fragment \(LET_{F}^+\) coincides with the degree-preserving logic of the involutive Stone algebras.
      PubDate: 2024-06-01
       
  • Intuitionistic Modal Algebras

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      Abstract: Abstract Recent research on algebraic models of quasi-Nelson logic has brought new attention to a number of classes of algebras which result from enriching (subreducts of) Heyting algebras with a special modal operator, known in the literature as a nucleus. Among these various algebraic structures, for which we employ the umbrella term intuitionistic modal algebras, some have been studied since at least the 1970s, usually within the framework of topology and sheaf theory. Others may seem more exotic, for their primitive operations arise from algebraic terms of the intuitionistic modal language which have not been previously considered. We shall for instance investigate the variety of weak implicative semilattices, whose members are (non-necessarily distributive) meet semilattices endowed with a nucleus and an implication operation which is not a relative pseudo-complement but satisfies the postulates of Celani and Jansana’s strict implication. For each of these new classes of algebras we establish a representation and a topological duality which generalize the known ones for Heyting algebras enriched with a nucleus.
      PubDate: 2024-06-01
       
  • De Morgan-Płonka Sums

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      Abstract: Abstract This paper develops De Morgan-Płonka sums, which generalise Płonka sums to contexts in which negation is not topically transparent but still respects De Morgan duality. We give a general theory of De Morgan-Płonka sums, on the model of the general theory of Płonka sums. Additionally, we describe free De Morgan-Płonka sums and apply our construction to give an algebraic proof of completeness for Kit Fine’s truthmaker semantics for Angell’s logic of analytic containment.
      PubDate: 2024-05-21
       
 
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