 Subjects -> PHILOSOPHY (Total: 762 journals)
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- Correction to: Group Representation for Even and Odd Involutive
Commutative Residuated Chains-
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PubDate: 2022-08-01
- Correction to: The Hahn Embedding Theorem for a Class of Residuated
Semigroups-
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Abstract: A Correction to this paper has been published: 10.1007/s11225-020-09933-y
PubDate: 2022-08-01
- A Modal View on Resource-Bounded Propositional Logics
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Abstract: Abstract Classical propositional logic plays a prominent role in industrial applications, and yet the complexity of this logic is presumed to be non-feasible. Tractable systems such as depth-bounded boolean logics approximate classical logic and can be seen as a model for resource-bounded agents whose reasoning style is nonetheless classical. In this paper we first study a hierarchy of tractable logics that is not defined by depth. Then we extend it into a modal logic where modalities make explicit the assumptions discharged in propositional proofs, thereby expressing blueprints for proofs. A natural deduction system is provided that permits to reason about and manage such proof blueprints.
PubDate: 2022-08-01
- Generalizing Deontic Action Logic
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Abstract: Abstract We introduce a multimodal framework of deontic action logic which encodes the interaction between two fundamental procedures in normative reasoning: conceptual classification and deontic classification. The expressive power of the framework is noteworthy, since it combines insights from agency logic and dynamic logic, allowing for a representation of many kinds of normative conflicts. We provide a semantic characterization for three axiomatic systems of increasing strength, showing how our approach can be modularly extended in order to get different levels of analysis of normative reasoning. Finally, we discuss ways in which the framework can be used to capture other formalisms proposed in the literature, as well as to model searching problems in Artificial Intelligence.
PubDate: 2022-08-01
- Group Representation for Even and Odd Involutive Commutative Residuated
Chains-
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Abstract: Abstract For odd and for even involutive, commutative residuated chains a representation theorem is presented in this paper by means of direct systems of abelian o-groups equipped with further structure. This generalizes the corresponding result of J. M. Dunnabout finite Sugihara monoids.
PubDate: 2022-08-01
- Simplified Kripke Semantics for K45-Like Gödel Modal Logics and Its
Axiomatic Extensions-
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Abstract: Abstract In this paper we provide a simplified, possibilistic semantics for the logics K45(G), i.e. a many-valued counterpart of the classical modal logic K45 over the [0, 1]-valued Gödel fuzzy logic \(\mathbf{G}\) . More precisely, we characterize K45(G) as the set of valid formulae of the class of possibilistic Gödel frames \(\langle W, \pi \rangle \) , where W is a non-empty set of worlds and \(\pi : W \mathop {\rightarrow }[0,1]\) is a possibility distribution on W. We provide decidability results as well. Moreover, we show that all the results also apply to the extension of K45(G) with the axiom (D), provided that we restrict ourselves to normalised Gödel Kripke frames, i.e. frames \(\langle W, \pi \rangle \) where \(\pi \) satisfies the normalisation condition \(\sup _{w \in W} \pi (w) = 1\) .
PubDate: 2022-08-01
- An Analysis of Poly-connexivity
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Abstract: Abstract Francez has suggested that connexivity can be predicated of connectives other than the conditional, in particular conjunction and disjunction. Since connexivity is not any connection between antecedents and consequents—there might be other connections among them, such as relevance—, my question here is whether Francez’s conjunction and disjunction can properly be called ‘connexive’. I analyze three ways in which those connectives may somehow inherit connexivity from the conditional by standing in certain relations to it. I will show that Francez’s connectives fail all these three ways, and that even other connectives obtained by following more closely Wansing’s method to get a connexive conditional, fail to be connexive as well.
PubDate: 2022-08-01
- Twist Structures and Nelson Conuclei
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Abstract: Abstract Motivated by Kalman residuated lattices, Nelson residuated lattices and Nelson paraconsistent residuated lattices, we provide a natural common generalization of them. Nelson conucleus algebras unify these examples and further extend them to the non-commutative setting. We study their structure, establish a representation theorem for them in terms of twist structures and conuclei that results in a categorical adjunction, and explore situations where the representation is actually an isomorphism. In the latter case, the adjunction is elevated to a categorical equivalence. By applying this representation to the original motivating special cases we bring to the surface their underlying similarities.
PubDate: 2022-08-01
- On Extracting Variable Herbrand Disjunctions
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Abstract: Abstract Some quantitative results obtained by proof mining take the form of Herbrand disjunctions that may depend on additional parameters. We attempt to elucidate this fact through an extension to first-order arithmetic of the proof of Herbrand’s theorem due to Gerhardy and Kohlenbach which uses the functional interpretation.
PubDate: 2022-08-01
- The G4i Analogue of a G3i Sequent Calculus
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Abstract: Abstract This paper provides a method to obtain terminating analytic calculi for a large class of intuitionistic modal logics. For a given logic L with a cut-free calculus G that is an extension of G3ip the method produces a terminating analytic calculus that is an extension of G4ip and equivalent to G. G4ip was introduced by Roy Dyckhoff in 1992 as a terminating analogue of the calculus G3ip for intuitionistic propositional logic. Thus this paper can be viewed as an extension of Dyckhoff’s work to intuitionistic modal logic.
PubDate: 2022-07-15
- On Relative Principal Congruences in Term Quasivarieties
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Abstract: Abstract Let \({\mathcal {K}}\) be a quasivariety. We say that \({\mathcal {K}}\) is a term quasivariety if there exist an operation of arity zero e and a family of binary terms \(\{t_i\}_{i\in I}\) such that for every \(A \in {\mathcal {K}}\) , \(\theta \) a \({\mathcal {K}}\) -congruence of A and \(a,b\in A\) the following condition is satisfied: \((a,b)\in \theta \) if and only if \((t_{i}(a,b),e) \in \theta \) for every \(i\in I\) . In this paper we study term quasivarieties. For every \(A\in {\mathcal {K}}\) and \(a,b\in A\) we present a description for the smallest \({\mathcal {K}}\) -congruence containing the pair (a, b). We apply this result in order to characterize \({\mathcal {K}}\) -compatible functions on A (i.e., functions which preserve all the \({\mathcal {K}}\) -congruences of A) and we give two applications of this property: (1) we give necessary conditions on \({\mathcal {K}}\) for which for every \(A \in {\mathcal {K}}\) the \({\mathcal {K}}\) -compatible functions on A coincides with a polynomial over finite subsets of A; (2) we give a method to build up \({\mathcal {K}}\) -compatible functions.
PubDate: 2022-07-07
- Logics of Order and Related Notions
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Abstract: Abstract The aim of the paper is twofold. First, we want to recapture the genesis of the logics of order. The origin of this notion is traced back to the work of Jerzy Kotas, Roman Suszko, Richard Routley and Robert K. Meyer. A further development of the theory of logics of order is presented in the papers of Jacek K. Kabziński. Quite contemporarily, this notion gained in significance in the papers of Carles Noguera and Petr Cintula. Logics of order are named there logics of weak implications. They play a crucial role in their monograph (Noguera and Cintula Logic and Implication. An Introduction to the General Algebraic Study of Non-Classical Logics, Trends in Logic 57, Springer, Berlin, 2021). But, more importantly, the other goal is to define some subclasses of the logics of order in reference to later results of Jacek K. Kabziński and Michael Dunn. The original conception of implication is due to Kabziński. Implication is a stronger notion than the notion of the connective of order aka weak implication. As a result, the three subclasses of logics of order are isolated: logics of implication, logics of symmetry, and tonoidal logics. These notions are uniformly defined and investigated from various viewpoints in terms of consequence operations. The emphasis is put on their semantics.
PubDate: 2022-06-28
- Nils Kürbis, Proof and Falsity: A Logical Investigation, Cambridge
University Press, 2019, pp. 316; ISBN: 978-110-87-1672-7
(Softcover)£24.99, ISBN: 978-110-84-8130-4 (Hardcover)£78.99, ISBN:
978-110-86-2517-3 (eBook) $26.00.-
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PubDate: 2022-06-11
- Natural Deduction Systems for Intuitionistic Logic with Identity
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Abstract: Abstract The aim of the paper is to present two natural deduction systems for Intuitionistic Sentential Calculus with Identity (ISCI); a syntactically motivated \(\mathsf {ND}^1_{\mathsf {ISCI}}\) and a semantically motivated \(\mathsf {ND}^2_{\mathsf {ISCI}}\) . The formulation of \(\mathsf {ND}^1_{\mathsf {ISCI}}\) is based on the axiomatic formulation of ISCI. Its rules cannot be straightforwardly classified as introduction or elimination rules; ISCI-specific rules are based on axioms characterizing the identity connective. The system does not enjoy the standard subformula property, but due to the normalization procedure non-subformulas can label only leaves of proofs. In \(\mathsf {ND}^2_{\mathsf {ISCI}}\) , we propose only two general identity-related rules, in reference to the treatment of the identity connective in First-Order Logic.
PubDate: 2022-06-11
- Correction to: Can Başkent, Thomas Macaulay Ferguson (eds.), Graham
Priest on Dialetheism and Paraconsistency, Springer International
Publishing, Outstanding Contributions to Logic, Vol. 18, 2019, pp. 704+xi;
ISBN 978-3-030-25367-7 (Softcover) 106.99 €, ISBN 978-3-030-25364-6
(Hardcover) 149.79 €.-
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Abstract: A Correction to this paper has been published: 10.1007/s11225-021-09980-z
PubDate: 2022-06-06
- Beishui Liao, Thomas Ågotnes, Yi N. Wang, (eds.), Dynamics, Uncertainty
and Reasoning, vol. 4 of Logic in Asia: Studia Logica Library, Springer,
Singapore, 2019, pp. 207+xii; ISBN: 978-981-13-7793-8 (Softcover) 117,69
€, ISBN: 978-981-13-7790-7 (Hardcover) 160,49 €, ISBN:
978-981-13-7791-4 (eBook) 93,08 €.-
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PubDate: 2022-06-06
- Correction to: Cut-free Sequent Calculus and Natural Deduction for the
Tetravalent Modal Logic-
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PubDate: 2022-06-01
DOI: 10.1007/s11225-021-09982-x
- Tableaux for Some Modal-Tense Logics Graham Priest’s Fashion
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Abstract: Abstract The forward convergence constraint is important to time analysis. Without it, given two future moments to the same point, the time branches. This is unacceptable if one assumes that time is linear. Nevertheless, one may wish to consider time-branching in order to discuss future possibilities. One can have both a linear order for the time and branching through the combination of the tense logic semantics with those of an alethic logic which allows the evaluation of the timelines of other possible worlds. In this paper, I give the semantics and the tableaux systems for some alethic-tense logics. I review one in which worlds differ on their time orders (MT), another in which they agree on the time order (MOT), a pair of conditional tense logics ( \(CT, CT^+\) ), and the first-order version of MT. A brief philosophical discussion arises from every system.
PubDate: 2022-06-01
DOI: 10.1007/s11225-021-09974-x
- Calculi of Epistemic Grounding Based on Prawitz’s Theory of Grounds
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Abstract: Abstract We define a class of formal systems inspired by Prawitz’s theory of grounds. The latter is a semantics that aims at accounting for epistemic grounding, namely, at explaining why and how deductively valid inferences have the power to epistemically compel to accept the conclusion. Validity is defined in terms of typed objects, called grounds, that reify evidence for given judgments. An inference is valid when a function exists from grounds for the premises to grounds for the conclusion. Grounds are described by formal terms, either directly when the terms are in canonical form, or indirectly when they are in non-canonical form. Non-canonical terms must reduce to canonical form, and two terms may be said to be equal when they converge towards equivalent grounds. In our systems these properties can be proved through rules distinguished according to whether they concern types or logic. Type rules involve type introduction and elimination, equality for application of operational symbols, and re-writing equations for non-canonical terms. The logic amounts to a sort of intuitionistic system in a Gentzen format. To conclude, we show that each system of our class enjoys a normalization property.
PubDate: 2022-06-01
DOI: 10.1007/s11225-021-09979-6
- Obituary
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PubDate: 2022-05-11
DOI: 10.1007/s11225-022-10005-6
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