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 [2467 journals] 
 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: 20230201

 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: 20230201

 Linear LAlgebras and Prime Factorization

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Abstract: Abstract A complete recursive description of noetherian linear KLalgebras is given. Lalgebras form a quantum structure that occurs in algebraic logic, combinatorial group theory, measure theory, geometry, and in connection with solutions to the YangBaxter equation. It is proved that the selfsimilar closure of a noetherian linear KLalgebra is determined by its partially ordered set of primes, and that its elements admit a unique factorization by a decreasing sequence of prime elements.
PubDate: 20230201

 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: 20230201

 Notes on Models of (Partial) Kripke–Feferman Truth

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Abstract: Abstract This article investigates models of axiomatizations related to the semantic conception of truth presented by Kripke (J Philos 72(19):690–716, 1975), the socalled fixedpoint semantics. Among the various proof systems devised as a prooftheoretic characterization of the fixedpoint semantics, in recent years two alternatives have received particular attention: classical systems (i.e., systems based on classical logic) and nonclassical systems (i.e., systems based on some nonclassical logic). The present article, building on Halbach and Nicolai (J Philos Log 47(2):227–257, 2018), shows that there is a sense in which classical and nonclassical theories (in suitable variants) have the same models.
PubDate: 20230201

 Intuitionistic Propositional Logic with Galois Negations

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Abstract: Abstract Intuitionistic propositional logic with Galois negations ( \(\mathsf {IGN}\) ) is introduced. Heyting algebras with Galois negations are obtained from Heyting algebras by adding the Galois pair \((\lnot ,{\sim })\) and dual Galois pair \((\dot{\lnot },\dot{\sim })\) of negations. Discrete duality between GNframes and algebras as well as the relational semantics for \(\mathsf {IGN}\) are developed. A Hilbertstyle axiomatic system \(\mathsf {HN}\) is given for \(\mathsf {IGN}\) , and Galois negation logics are defined as extensions of \(\mathsf {IGN}\) . We give the bitense logic \(\mathsf {S4N}_t\) which is obtained from the minimal tense extension of the modal logic \(\mathsf {S4}\) by adding tense operators. We give a new extended Gödel translation \(\tau \) and prove that \(\mathsf {IGN}\) is embedded into \(\mathsf {S4N}_t\) by \(\tau \) . Moreover, every Kripkecomplete Galois negation logic L is embedded into its tense companion \(\tau (L)\) .
PubDate: 20230201

 Birkhoff’s and Mal’cev’s Theorems for Implicational
Tonoid Logics
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Abstract: Abstract In the context of implicational tonoid logics, this paper investigates analogues of Birkhoff’s two theorems, the socalled subdirect representation and varieties theorems, and of Mal’cev’s quasivarieties theorem. More precisely, we first recall the class of implicational tonoid logics. Next, we establish the subdirect product representation theorem for those logics and then consider some more related results such as completeness. Thirdly, we consider the varieties theorem for them. Finally, we introduce an analogue of Mal’cev’s quasivarieties theorem for algebras.
PubDate: 20230131

 Semantical Analysis of the Logic of Bunched Implications

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Abstract: Abstract We give a novel approach to proving soundness and completeness for a logic (henceforth: the objectlogic) that bypasses truthinamodel to work directly with validity. Instead of working with specific worlds in specific models, we reason with eigenworlds (i.e., generic representatives of worlds) in an arbitrary model. This reasoning is captured by a sequent calculus for a metalogic (in this case, firstorder classical logic) expressive enough to capture the semantics of the objectlogic. Essentially, one has a calculus of validity for the objectlogic. The method proceeds through the perspective of reductive logic (as opposed to the more traditional paradigm of deductive logic), using the space of reductions as a medium for showing the behavioural equivalence of reduction in the sequent calculus for the objectlogic and in the validity calculus. Rather than study the technique in general, we illustrate it for the logic of Bunched Implications (BI), thus IPL and MILL (without negation) are also treated. Intuitively, BI is the free combination of intuitionistic propositional logic and multiplicative intuitionistic linear logic, which renders its metatheory is quite complex. The literature on BI contains many similar, but ultimately different, algebraic structures and satisfaction relations that either capture only fragments of the logic (albeit large ones) or have complex clauses for certain connectives (e.g., Beth’s clause for disjunction instead of Kripke’s). It is this complexity that motivates us to use BI as a casestudy for this approach to semantics.
PubDate: 20230131

 On Boolean Algebraic Structure of Proofs: Towards an Algebraic Semantics
for the Logic of Proofs
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Abstract: Abstract We present algebraic semantics for the classical logic of proofs based on Boolean algebras. We also extend the language of the logic of proofs in order to have a Boolean structure on proof terms and equality predicate on terms. Moreover, the completeness theorem and certain generalizations of Stone’s representation theorem are obtained for all proposed algebras.
PubDate: 20230131

 An Axiomatic System for Concessive Conditionals

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Abstract: Abstract According to the analysis of concessive conditionals suggested by Crupi and Iacona, a concessive conditional \(p{{\,\mathrm{\hookrightarrow }\,}}q\) is adequately formalized as a conjunction of conditionals. This paper presents a sound and complete axiomatic system for concessive conditionals so understood. The soundness and completeness proofs that will be provided rely on a method that has been employed by Raidl, Iacona, and Crupi to prove the soundness and completeness of an analogous system for evidential conditionals.
PubDate: 20230131

 Everyone Knows That Everyone Knows: Gossip Protocols for Super Experts

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Abstract: Abstract A gossip protocol is a procedure for sharing secrets in a network. The basic action in a gossip protocol is a pairwise message exchange (telephone call) wherein the calling agents exchange all the secrets they know. An agent who knows all secrets is an expert. The usual termination condition is that all agents are experts. Instead, we explore protocols wherein the termination condition is that all agents know that all agents are experts. We call such agents super experts. We also investigate gossip protocols that are common knowledge among the agents. Additionally, we model that agents who are super experts do not make and do not answer calls, and that this is common knowledge. We investigate conditions under which protocols terminate, both in the synchronous case, where there is a global clock, and in the asynchronous case, where there is not. We show that a commonly known protocol with engaged agents may terminate faster than the same commonly known protocol without engaged agents.
PubDate: 20230130

 Stefano Bonzio, Francesco Paoli, Michele Pra Baldi, Logics of Variable
Inclusion, vol. 59 of Trends in Logic, Springer, 2022, pp. 221+x; ISBN:
9783031042966 (Hardcover) 106.99€, ISBN: 9783031042997 (eBook)
85.59€.
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PubDate: 20230112

 SubHilbert Lattices

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Abstract: Abstract A hemiimplicative lattice is an algebra \((A,\wedge ,\vee ,\rightarrow ,1)\) of type (2, 2, 2, 0) such that \((A,\wedge ,\vee ,1)\) is a lattice with top and for every \(a,b\in A\) , \(a\rightarrow a = 1\) and \(a\wedge (a\rightarrow b) \le b\) . A new variety of hemiimplicative lattices, here named subHilbert lattices, containing both the variety generated by the \(\{\wedge ,\vee ,\rightarrow ,1\}\) reducts of subresiduated lattices and that of Hilbert lattices as proper subvarieties is defined. It is shown that any subHilbert lattice is determined (up to isomorphism) by a triple (L, D, S) which satisfies the following conditions: L is a bounded distributive lattice, D is a sublattice of L containing 0, 1 such that for each \(a, b \in L\) there is an element \(c \in D\) with the property that for all \(d \in D\) , \(a \wedge d \le b\) if and only if \(d \le c\) (we write \(a \rightarrow _D b\) for the element c), and S is a non void subset of L such that S is closed under \(\rightarrow _D\) and S, with its inherited order, is itself a lattice. Finally, the congruences of subHilbert lattices are studied.
PubDate: 20230103

 The Elimination of Maximum Cuts in Linear Logic and BCK Logic

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Abstract: Abstract In the sequent systems for exponentialfree linear logic and BCK logic a procedure of elimination of maximum cuts, cuts which correspond to maximum segments from natural deduction derivations, will be presented.
PubDate: 20221215

 Correction to: A Modal View on ResourceBounded Propositional Logics

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PubDate: 20221201

 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: 20221201

 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: 20221201

 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: 20221201

 Hilbert Algebras with Hilbert–Galois Connections

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Abstract: Abstract In this paper we introduce Hilbert algebras with Hilbert–Galois connections (HilGCalgebras) and we study the Hilbert–Galois connections defined in Heyting algebras, called HGCalgebras. We assign a categorical duality between the category HilGCalgebras with Hilbert homomorphisms that commutes with Hilbert–Galois connections and Hilbert spaces with certain binary relations and whose morphisms are special functional relations. We also prove a categorical duality between the category of Heyting Galois algebras with Heyting homomorphisms that commutes with Hilbert–Galois connections and the category of spectral Heyting spaces endowed with a binary relation with certain special continuous maps.
PubDate: 20221025
DOI: 10.1007/s11225022100190

 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
DOI: 10.1007/s11225022100109
