Studia Logica
Journal Prestige (SJR): 0.353 Citation Impact (citeScore): 1 Number of Followers: 3 Hybrid journal (It can contain Open Access articles) ISSN (Print) 15728730  ISSN (Online) 00393215 Published by SpringerVerlag [2469 journals] 
 Discrete Duality for Nelson Algebras with Tense Operators

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Abstract: Abstract In this paper, we continue with the study of tense operators on Nelson algebras (Figallo et al. in Studia Logica 109(2):285–312, 2021, Studia Logica 110(1):241–263, 2022). We define the variety of algebras, which we call tense Nelson Dalgebras, as a natural extension of tense De Morgan algebras (Figallo and Pelaitay in Logic J IGPL 22(2):255–267, 2014). In particular, we give a discrete duality for these algebras. To do this, we will extend the representation theorems for Nelson algebras given in Sendlewski (Studia Logica 43(3):257–280, 1984) to the tense case.
PubDate: 20220921

 LoopCheck Specification for a Sequent Calculus of Temporal Logic

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Abstract: Abstract In our previous work we have introduced looptype sequent calculi for propositional linear discrete tense logic and proved that these calculi are sound and complete. Decision procedures using the calculi have been constructed for the considered logic. In the present paper we restrict ourselves to the logic with the unary temporal operators “next” and “henceforth always”. Prooftheory of the sequent calculus of this logic is considered, focusing on loop specification in backward proofsearch. We describe cyclic sequents and prove that any loop consists of only cyclic sequents. A class of sequents for which backward proofsearch do not require loopcheck is presented. It is shown how sequents can be coded by binary strings that are used in backward proofsearch for the sake of more efficient loopcheck.
PubDate: 20220830

 Correction to: Group Representation for Even and Odd Involutive
Commutative Residuated Chains
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PubDate: 20220801
DOI: 10.1007/s11225022099914

 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/s1122502009933y
PubDate: 20220801
DOI: 10.1007/s11225022099861

 A Modal View on ResourceBounded 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 nonfeasible. Tractable systems such as depthbounded boolean logics approximate classical logic and can be seen as a model for resourcebounded 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: 20220801
DOI: 10.1007/s11225022099843

 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: 20220801
DOI: 10.1007/s1122502209989y

 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 ogroups equipped with further structure. This generalizes the corresponding result of J. M. Dunnabout finite Sugihara monoids.
PubDate: 20220801
DOI: 10.1007/s1122502109981y

 Simplified Kripke Semantics for K45Like 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 manyvalued 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 nonempty 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: 20220801
DOI: 10.1007/s11225022099870

 An Analysis of Polyconnexivity

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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: 20220801
DOI: 10.1007/s11225022099852

 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 noncommutative 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: 20220801
DOI: 10.1007/s1122502209988z

 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 firstorder arithmetic of the proof of Herbrand’s theorem due to Gerhardy and Kohlenbach which uses the functional interpretation.
PubDate: 20220801
DOI: 10.1007/s11225022099905

 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 cutfree 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: 20220715
DOI: 10.1007/s11225022100083

 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: 20220707
DOI: 10.1007/s11225022100118

 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 NonClassical 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: 20220628
DOI: 10.1007/s11225022100092

 Nils Kürbis, Proof and Falsity: A Logical Investigation, Cambridge
University Press, 2019, pp. 316; ISBN: 9781108716727
(Softcover)£24.99, ISBN: 9781108481304 (Hardcover)£78.99, ISBN:
9781108625173 (eBook) $26.00.
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PubDate: 20220611
DOI: 10.1007/s11225022100029

 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; ISCIspecific rules are based on axioms characterizing the identity connective. The system does not enjoy the standard subformula property, but due to the normalization procedure nonsubformulas can label only leaves of proofs. In \(\mathsf {ND}^2_{\mathsf {ISCI}}\) , we propose only two general identityrelated rules, in reference to the treatment of the identity connective in FirstOrder Logic.
PubDate: 20220611
DOI: 10.1007/s11225022099950

 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 9783030253677 (Softcover) 106.99 €, ISBN 9783030253646
(Hardcover) 149.79 €.
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Abstract: A Correction to this paper has been published: 10.1007/s1122502109980z
PubDate: 20220606
DOI: 10.1007/s1122502209999w

 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: 9789811377938 (Softcover) 117,69
€, ISBN: 9789811377907 (Hardcover) 160,49 €, ISBN:
9789811377914 (eBook) 93,08 €.
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PubDate: 20220606
DOI: 10.1007/s1122502209996z

 Correction to: Cutfree Sequent Calculus and Natural Deduction for the
Tetravalent Modal Logic
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PubDate: 20220601
DOI: 10.1007/s1122502109982x

 Obituary

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PubDate: 20220511
DOI: 10.1007/s11225022100056
