-
Non-Reflexive Nonsense: Proof Theory of Paracomplete Weak Kleene Logic Stud. Log. (IF 0.7) Pub Date : 2024-03-18
Abstract Our aim is to provide a sequent calculus whose external consequence relation coincides with the three-valued paracomplete logic ‘of nonsense’ introduced by Dmitry Bochvar and, independently, presented as the weak Kleene logic \(\textbf{K}_{\textbf{3}}^{\textbf{w}}\) by Stephen C. Kleene. The main features of this calculus are (i) that it is non-reflexive, i.e., Identity is not included as
-
Finite Hilbert Systems for Weak Kleene Logics Stud. Log. (IF 0.7) Pub Date : 2024-03-16
Abstract Multiple-conclusion Hilbert-style systems allow us to finitely axiomatize every logic defined by a finite matrix. Having obtained such axiomatizations for Paraconsistent Weak Kleene and Bochvar–Kleene logics, we modify them by replacing the multiple-conclusion rules with carefully selected single-conclusion ones. In this way we manage to introduce the first finite Hilbert-style single-conclusion
-
Jaśkowski and the Jains Stud. Log. (IF 0.7) Pub Date : 2024-03-13 Graham Priest
In 1948 Jaśkowski introduced the first discussive logic. The main technical idea was to take what holds to be what is true at some possible world. Some 2,000 years earlier, Jain philosophers had advocated a similar idea, in their doctrine of syādvāda. Of course, these philosophers had no knowledge of contemporary logical notions; but the techniques pioneered by Jaśkowski can be deployed to make the
-
On Geometric Implications Stud. Log. (IF 0.7) Pub Date : 2024-03-06
Abstract It is a well-known fact that although the poset of open sets of a topological space is a Heyting algebra, its Heyting implication is not necessarily stable under the inverse image of continuous functions and hence is not a geometric concept. This leaves us wondering if there is any stable family of implications that can be safely called geometric. In this paper, we will first recall the abstract
-
Kripke-Completeness and Sequent Calculus for Quasi-Boolean Modal Logic Stud. Log. (IF 0.7) Pub Date : 2024-03-06
Abstract Quasi-Boolean modal algebras are quasi-Boolean algebras with a modal operator satisfying the interaction axiom. Sequential quasi-Boolean modal logics and the relational semantics are introduced. Kripke-completeness for some quasi-Boolean modal logics is shown by the canonical model method. We show that every descriptive persistent quasi-Boolean modal logic is canonical. The finite model property
-
Variations on the Kripke Trick Stud. Log. (IF 0.7) Pub Date : 2024-03-06
Abstract In the early 1960s, to prove undecidability of monadic fragments of sublogics of the predicate modal logic \(\textbf{QS5}\) that include the classical predicate logic \(\textbf{QCl}\) , Saul Kripke showed how a classical atomic formula with a binary predicate letter can be simulated by a monadic modal formula. We consider adaptations of Kripke’s simulation, which we call the Kripke trick,
-
Angell and McCall Meet Wansing Stud. Log. (IF 0.7) Pub Date : 2024-02-17 Hitoshi Omori, Andreas Kapsner
In this paper, we introduce a new logic, which we call AM3. It is a connexive logic that has several interesting properties, among them being strongly connexive and validating the Converse Boethius Thesis. These two properties are rather characteristic of the difference between, on the one hand, Angell and McCall’s CC1 and, on the other, Wansing’s C. We will show that in other aspects, as well, AM3
-
Independence Results for Finite Set Theories in Well-Founded Locally Finite Graphs Stud. Log. (IF 0.7) Pub Date : 2024-02-16
Abstract We consider all combinatorially possible systems corresponding to subsets of finite set theory (i.e., Zermelo-Fraenkel set theory without the axiom of infinity) and for each of them either provide a well-founded locally finite graph that is a model of that theory or show that this is impossible. To that end, we develop the technique of axiom closure of graphs.
-
Ecumenical Propositional Tableau Stud. Log. (IF 0.7) Pub Date : 2024-02-16
Abstract Ecumenical logic aims to peacefully join classical and intuitionistic logic systems, allowing for reasoning about both classical and intuitionistic statements. This paper presents a semantic tableau for propositional ecumenical logic and proves its soundness and completeness concerning Ecumenical Kripke models. We introduce the Ecumenical Propositional Tableau ( \(E_T\) ) and demonstrate its
-
On Woodruff’s Constructive Nonsense Logic Stud. Log. (IF 0.7) Pub Date : 2024-01-22 Jonas R. B. Arenhart, Hitoshi Omori
Sören Halldén’s logic of nonsense is one of the most well-known many-valued logics available in the literature. In this paper, we discuss Peter Woodruff’s as yet rather unexplored attempt to advance a version of such a logic built on the top of a constructive logical basis. We start by recalling the basics of Woodruff’s system and by bringing to light some of its notable features. We then go on to
-
Proof-Theoretic Aspects of Paraconsistency with Strong Consistency Operator Stud. Log. (IF 0.7) Pub Date : 2024-01-13 Victoria Arce Pistone, Martín Figallo
In order to develop efficient tools for automated reasoning with inconsistency (theorem provers), eventually making Logics of Formal inconsistency (LFI) a more appealing formalism for reasoning under uncertainty, it is important to develop the proof theory of the first-order versions of such LFIs. Here, we intend to make a first step in this direction. On the other hand, the logic Ciore was developed
-
An $$\omega $$ -Rule for the Logic of Provability and Its Models Stud. Log. (IF 0.7) Pub Date : 2024-01-09 Katsumi Sasaki, Yoshihito Tanaka
In this paper, we discuss semantical properties of the logic \(\textbf{GL}\) of provability. The logic \(\textbf{GL}\) is a normal modal logic which is axiomatized by the the Löb formula \( \Box (\Box p\supset p)\supset \Box p \), but it is known that \(\textbf{GL}\) can also be axiomatized by an axiom \(\Box p\supset \Box \Box p\) and an \(\omega \)-rule \((\Diamond ^{*})\) which takes countably many
-
Nelson Conuclei and Nuclei: The Twist Construction Beyond Involutivity Stud. Log. (IF 0.7) Pub Date : 2024-01-09
Abstract Recent work by Busaniche, Galatos and Marcos introduced a very general twist construction, based on the notion of conucleus, which subsumes most existing approaches. In the present paper we extend this framework one step further, so as to allow us to construct and represent algebras which possess a negation that is not necessarily involutive. Our aim is to capture the main properties of the
-
Combining Intuitionistic and Classical Propositional Logic: Gentzenization and Craig Interpolation Stud. Log. (IF 0.7) Pub Date : 2024-01-06
Abstract This paper studies a combined system of intuitionistic and classical propositional logic from proof-theoretic viewpoints. Based on the semantic treatment of Humberstone (J Philos Log 8:171–196, 1979) and del Cerro and Herzig (Frontiers of combining systems: FroCoS, Springer, 1996), a sequent calculus \(\textsf{G}(\textbf{C}+\textbf{J})\) is proposed. An approximate idea of obtaining \(\te
-
Connexive Logic, Connexivity, and Connexivism: Remarks on Terminology Stud. Log. (IF 0.7) Pub Date : 2023-12-09 Heinrich Wansing, Hitoshi Omori
Over the past ten years, the community researching connexive logics is rapidly growing and a number of papers have been published. However, when it comes to the terminology used in connexive logic, it seems to be not without problems. In this introduction, we aim at making a contribution towards both unifying and reducing the terminology. We hope that this can help making it easier to survey and access
-
The Logic ILP for Intuitionistic Reasoning About Probability Stud. Log. (IF 0.7) Pub Date : 2023-12-09 Angelina Ilić-Stepić, Zoran Ognjanović, Aleksandar Perović
We offer an alternative approach to the existing methods for intuitionistic formalization of reasoning about probability. In terms of Kripke models, each possible world is equipped with a structure of the form \(\langle H, \mu \rangle \) that needs not be a probability space. More precisely, though H needs not be a Boolean algebra, the corresponding monotone function (we call it measure) \(\mu : H
-
Quineanism, Noneism and Metaphysical Equivalence Stud. Log. (IF 0.7) Pub Date : 2023-12-09 Bruno Jacinto, Javier Belastegui
In this paper we propose and defend the Synonymy account, a novel account of metaphysical equivalence which draws on the idea (Rayo in The Construction of Logical Space, Oxford University Press, Oxford, 2013) that part of what it is to formulate a theory is to lay down a theoretical hypothesis concerning logical space. Roughly, two theories are synonymous—and so, in our view, equivalent—just in case
-
Representability of Kleene Posets and Kleene Lattices Stud. Log. (IF 0.7) Pub Date : 2023-12-08 Ivan Chajda, Helmut Länger, Jan Paseka
A Kleene lattice is a distributive lattice equipped with an antitone involution and satisfying the so-called normality condition. These lattices were introduced by J. A. Kalman. We extended this concept also for posets with an antitone involution. In our recent paper (Chajda, Länger and Paseka, in: Proceeding of 2022 IEEE 52th International Symposium on Multiple-Valued Logic, Springer, 2022), we showed
-
On Pretabular Extensions of Relevance Logic Stud. Log. (IF 0.7) Pub Date : 2023-11-16 Asadollah Fallahi, James Gordon Raftery
We exhibit infinitely many semisimple varieties of semilinear De Morgan monoids (and likewise relevant algebras) that are not tabular, but which have only tabular proper subvarieties. Thus, the extension of relevance logic by the axiom \((p\rightarrow q)\vee (q\rightarrow p)\) has infinitely many pretabular axiomatic extensions, regardless of the presence or absence of Ackermann constants.
-
A Logical Theory for Conditional Weak Ontic Necessity in Branching Time Stud. Log. (IF 0.7) Pub Date : 2023-11-14 Fengkui Ju
Weak ontic necessity is the ontic necessity expressed by “should” or “ought to”. An example of it is “I should be dead by now”. A feature of this necessity is that whether it holds is irrelevant to whether its underlying proposition holds. This necessity essentially involves time. This paper presents a logic for conditional weak ontic necessity in branching time. The logic’s language includes the next
-
A Generalization of Beall’s Off-Topic Interpretation Stud. Log. (IF 0.7) Pub Date : 2023-11-14 Yang Song, Hitoshi Omori, Jonas R. B. Arenhart, Satoshi Tojo
In one of his papers, JC Beall advanced a new and interesting interpretation of Weak Kleene logic, in terms of on-topic/off-topic. In brief, Beall suggests to read the third value as off-topic, whereas the two classical values are read as true and on-topic and false and on-topic. Building on Beall’s new interpretation, the aim of this paper is threefold. First, we discuss two motivations to enrich
-
On a Class of Subreducts of the Variety of Integral srl-Monoids and Related Logics Stud. Log. (IF 0.7) Pub Date : 2023-11-10 Juan Manuel Cornejo, Hernn Javier San Martín, Valeria Sígal
An integral subresiduated lattice ordered commutative monoid (or integral srl-monoid for short) is a pair \(({\textbf {A}},Q)\) where \({\textbf {A}}=(A,\wedge ,\vee ,\cdot ,1)\) is a lattice ordered commutative monoid, 1 is the greatest element of the lattice \((A,\wedge ,\vee )\) and Q is a subalgebra of A such that for each \(a,b\in A\) the set \(\{q \in Q: a \cdot q \le b\}\) has maximum, which
-
Connexive Negation Stud. Log. (IF 0.7) Pub Date : 2023-11-10 Luis Estrada-González, Ricardo Arturo Nicolás-Francisco
Seen from the point of view of evaluation conditions, a usual way to obtain a connexive logic is to take a well-known negation, for example, Boolean negation or de Morgan negation, and then assign special properties to the conditional to validate Aristotle’s and Boethius’ Theses. Nonetheless, another theoretical possibility is to have the extensional or the material conditional and then assign special
-
Substructural Nuclear (Image-Based) Logics and Operational Kripke-Style Semantics Stud. Log. (IF 0.7) Pub Date : 2023-10-16 Eunsuk Yang
This paper deals with substructural nuclear (image-based) logics and their algebraic and Kripke-style semantics. More precisely, we first introduce a class of substructural logics with connective N satisfying nucleus property, called here substructural nuclear logics, and its subclass, called here substructural nuclear image-based logics, where N further satisfies homomorphic image property. We then
-
Profinite Locally Finite Quasivarieties Stud. Log. (IF 0.7) Pub Date : 2023-10-16 Anvar M. Nurakunov, Marina V. Schwidefsky
Let \(\textbf{K}\) and \(\textbf{M}\) be locally finite quasivarieties of finite type such that \(\textbf{K}\subset \textbf{M}\). If \(\textbf{K}\) is profinite then the filter \([\textbf{K},\textbf{M}]\) in the quasivariety lattice \(\textrm{Lq}(\textbf{M})\) is an atomic lattice and \(\textbf{K}\) has an independent quasi-equational basis relative to \(\textbf{M}\). Applications of these results
-
Difference-Making Conditionals and Connexivity Stud. Log. (IF 0.7) Pub Date : 2023-10-10 Hans Rott
Today there is a wealth of fascinating studies of connexive logical systems. But sometimes it looks as if connexive logic is still in search of a convincing interpretation that explains in intuitive terms why the connexive principles should be valid. In this paper I argue that difference-making conditionals as presented in Rott (Review of Symbolic Logic 15, 2022) offer one principled way of interpreting
-
Heyting $$\kappa $$ -Frames Stud. Log. (IF 0.7) Pub Date : 2023-10-07 Hector Freytes, Giuseppe Sergioli
In the framework of algebras with infinitary operations, the equational theory of \(\bigvee _{\kappa }\)-complete Heyting algebras or Heyting \(\kappa \)-frames is studied. A Hilbert style calculus algebraizable in this class is formulated. Based on the infinitary structure of Heyting \(\kappa \)-frames, an equational type completeness theorem related to the \(\langle \bigvee , \wedge , \rightarrow
-
Sets with Dependent Elements: A Formalization of Castoriadis’ Notion of Magma Stud. Log. (IF 0.7) Pub Date : 2023-09-28 Athanassios Tzouvaras
We present a formalization of collections that Cornelius Castoriadis calls “magmas”, especially the property which mainly characterizes them and distinguishes them from the usual cantorian sets. It is the property of their elements to depend on other elements, either in a one-way or a two-way manner, so that one cannot occur in a collection without the occurrence of those dependent on it. Such a dependence
-
Semisimplicity and Congruence 3-Permutabilty for Quasivarieties with Equationally Definable Principal Congruences Stud. Log. (IF 0.7) Pub Date : 2023-09-20 Miguel Campercholi, Diego Vaggione
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
-
Boolean Connexive Logic and Content Relationship Stud. Log. (IF 0.7) Pub Date : 2023-09-20 Mateusz Klonowski, Luis Estrada-González
We present here some Boolean connexive logics (BCLs) that are intended to be connexive counterparts of selected Epstein’s content relationship logics (CRLs). The main motivation for analyzing such logics is to explain the notion of connexivity by means of the notion of content relationship. The article consists of two parts. In the first one, we focus on the syntactic analysis by means of axiomatic
-
Unary Interpretability Logics for Sublogics of the Interpretability Logic $$\textbf{IL}$$ Stud. Log. (IF 0.7) Pub Date : 2023-09-20 Yuya Okawa
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 \(\textbf{IL}\).
-
Intuitionistic Public Announcement Logic with Distributed Knowledge Stud. Log. (IF 0.7) Pub Date : 2023-09-15 Ryo Murai, Katsuhiko Sano
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
-
Intuitionistic Modal Algebras Stud. Log. (IF 0.7) Pub Date : 2023-09-15 Sergio A. Celani, Umberto Rivieccio
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
-
Decidability of Lattice Equations Stud. Log. (IF 0.7) Pub Date : 2023-09-15 Nikolaos Galatos
We provide an alternative proof of the decidability of the equational theory of lattices. The proof presented here is quite short and elementary.
-
Correspondence Theory for Modal Fairtlough–Mendler Semantics of Intuitionistic Modal Logic Stud. Log. (IF 0.7) Pub Date : 2023-08-29 Zhiguang Zhao
We study the correspondence theory of intuitionistic modal logic in modal Fairtlough–Mendler semantics (modal FM semantics) (Fairtlough and Mendler in Inf Comput 137(1):1–33, 1997), which is the intuitionistic modal version of possibility semantics (Holliday in UC Berkeley working paper in logic and the methodology of science, 2022. http://escholarship.org/uc/item/881757qn). We identify the fragment
-
Systems for Non-Reflexive Consequence Stud. Log. (IF 0.7) Pub Date : 2023-08-10 Carlo Nicolai, Lorenzo Rossi
Substructural logics and their application to logical and semantic paradoxes have been extensively studied. In the paper, we study theories of naïve consequence and truth based on a non-reflexive logic. We start by investigating the semantics and the proof-theory of a system based on schematic rules for object-linguistic consequence. We then develop a fully compositional theory of truth and consequence
-
From Belnap-Dunn Four-Valued Logic to Six-Valued Logics of Evidence and Truth Stud. Log. (IF 0.7) Pub Date : 2023-08-09 Marcelo E. Coniglio, Abilio Rodrigues
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
-
The Elimination of Direct Self-reference Stud. Log. (IF 0.7) Pub Date : 2023-08-03 Qianli Zeng, Ming Hsiung
This paper provides a procedure which, from any Boolean system of sentences, outputs another Boolean system called the ‘m-cycle unwinding’ of the original Boolean system for any positive integer m. We prove that for all \(m>1\), this procedure eliminates the direct self-reference in that the m-cycle unwinding of any Boolean system must be indirectly self-referential. More importantly, this procedure
-
Executability and Connexivity in an Interpretation of Griss Stud. Log. (IF 0.7) Pub Date : 2023-07-05 Thomas M. Ferguson
Although the work of G.F.C. Griss is commonly understood as a program of negationless mathematics, close examination of Griss’s work suggests a more fundamental feature is its executability, a requirement that mental constructions are possible only if corresponding mental activity can be actively carried out. Emphasizing executability reveals that Griss’s arguments against negation leave open several
-
A Simple Way to Overcome Hyperconnexivity Stud. Log. (IF 0.7) Pub Date : 2023-07-05 Alex Belikov
The term ‘hyperconnexive logic’ (or ‘hyperconnexivity’ in general) in relation to a certain logical system was coined by Sylvan to indicate that not only do Boethius’ theses hold in such a system, but also their converses. The plausibility of the latter was questioned by some connexive logicians. Without going into the discussion regarding the plausibility of hyperconnexivity and the converses of Boethius’
-
Connexive Logic, Probabilistic Default Reasoning, and Compound Conditionals Stud. Log. (IF 0.7) Pub Date : 2023-06-29 Niki Pfeifer, Giuseppe Sanfilippo
We present two approaches to investigate the validity of connexive principles and related formulas and properties within coherence-based probability logic. Connexive logic emerged from the intuition that conditionals of the form if not-A, then A, should not hold, since the conditional’s antecedent not-A contradicts its consequent A. Our approaches cover this intuition by observing that the only coherent
-
An Algebraic Investigation of the Connexive Logic $$\textsf{C}$$ Stud. Log. (IF 0.7) Pub Date : 2023-06-21 Davide Fazio, Sergei P. Odintsov
In this paper we show that axiomatic extensions of H. Wansing’s connexive logic \(\textsf{C}\) (\(\textsf{C}^{\perp }\)) are algebraizable (in the sense of J.W. Blok and D. Pigozzi) with respect to sub-varieties of \(\textsf{C}\)(\(\textsf{C}^{\perp }\))-algebras. We develop the structure theory of \(\textsf{C}\)(\(\textsf{C}^{\perp }\))-algebras, and we prove their representability in terms of twist-like
-
FMP-Ensuring Logics, RA-Ensuring Logics and FA-Ensuring Logics in $$\text {NExtK4.3}$$ Stud. Log. (IF 0.7) Pub Date : 2023-06-19 Ming Xu
This paper studies modal logics whose extensions all have the finite model property, those whose extensions are all recursively axiomatizable, and those whose extensions are all finitely axiomatizable. We call such logics FMP-ensuring, RA-ensuring and FA-ensuring respectively, and prove necessary and sufficient conditions of such logics in \(\mathsf {NExtK4.3}\). Two infinite descending chains \(\
-
On Heyting Algebras with Negative Tense Operators Stud. Log. (IF 0.7) Pub Date : 2023-06-14 Federico G. Almiñana, Gustavo Pelaitay, William Zuluaga
In this paper, we will study Heyting algebras endowed with tense negative operators, which we call tense H-algebras and we proof that these algebras are the algebraic semantics of the Intuitionistic Propositional Logic with Galois Negations. Finally, we will develop a Priestley-style duality for tense H-algebras.
-
Refutation-Aware Gentzen-Style Calculi for Propositional Until-Free Linear-Time Temporal Logic Stud. Log. (IF 0.7) Pub Date : 2023-06-14 Norihiro Kamide
This study introduces refutation-aware Gentzen-style sequent calculi and Kripke-style semantics for propositional until-free linear-time temporal logic. The sequent calculi and semantics are constructed on the basis of the refutation-aware setting for Nelson’s paraconsistent logic. The cut-elimination and completeness theorems for the proposed sequent calculi and semantics are proven.
-
Proof Systems for Super- Strict Implication Stud. Log. (IF 0.7) Pub Date : 2023-06-05 Guido Gherardi, Eugenio Orlandelli, Eric Raidl
This paper studies proof systems for the logics of super-strict implication \(\textsf{ST2}\)–\(\textsf{ST5}\), which correspond to C.I. Lewis’ systems \(\textsf{S2}\)–\(\textsf{S5}\) freed of paradoxes of strict implication. First, Hilbert-style axiomatic systems are introduced and shown to be sound and complete by simulating \(\textsf{STn}\) in \(\textsf{Sn}\) and backsimulating \(\textsf{Sn}\) in
-
Axiomatizing a Minimal Discussive Logic Stud. Log. (IF 0.7) Pub Date : 2023-05-29 Oleg Grigoriev, Marek Nasieniewski, Krystyna Mruczek-Nasieniewska, Yaroslav Petrukhin, Vasily Shangin
In the paper we analyse the problem of axiomatizing the minimal variant of discussive logic denoted as \( {\textsf {D}}_{\textsf {0}}\). Our aim is to give its axiomatization that would correspond to a known axiomatization of the original discussive logic \( {\textsf {D}}_{\textsf {2}}\). The considered system is minimal in a class of discussive logics. It is defined similarly, as Jaśkowski’s logic
-
Situation-Based Connexive Logic Stud. Log. (IF 0.7) Pub Date : 2023-05-29 Alessandro Giordani
The aim of this paper is to present a system of modal connexive logic based on a situation semantics. In general, modal connexive logics are extensions of standard modal logics that incorporate Aristotle’s and Boethius’ theses, that is the thesis that a sentence cannot imply its negation and the thesis that a sentence cannot imply a pair of contradictory sentences. A key problem in devising a connexive
-
$$\varvec{Brings~It~About~That}$$ Operators Decomposed with Relating Semantics Stud. Log. (IF 0.7) Pub Date : 2023-05-25 Tomasz Jarmużek, Mateusz Klonowski, Piotr Kulicki
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
-
A Simple Logic of the Hide and Seek Game Stud. Log. (IF 0.7) Pub Date : 2023-05-17 Dazhu Li, Sujata Ghosh, Fenrong Liu, Yaxin Tu
We discuss a simple logic to describe one of our favourite games from childhood, hide and seek, and show how a simple addition of an equality constant to describe the winning condition of the seeker makes our logic undecidable. There are certain decidable fragments of first-order logic which behave in a similar fashion with respect to such a language extension, and we add a new modal variant to that
-
Intuitionistic Logic is a Connexive Logic Stud. Log. (IF 0.7) Pub Date : 2023-05-02 Davide Fazio, Antonio Ledda, Francesco Paoli
We show that intuitionistic logic is deductively equivalent to Connexive Heyting Logic (\(\textrm{CHL}\)), hereby introduced as an example of a strongly connexive logic with an intuitive semantics. We use the reverse algebraisation paradigm: \(\textrm{CHL}\) is presented as the assertional logic of a point regular variety (whose structure theory is examined in detail) that turns out to be term equivalent
-
Connexivity in the Logic of Reasons Stud. Log. (IF 0.7) Pub Date : 2023-04-26 Andrea Iacona
This paper discusses some key connexive principles construed as principles about reasons, that is, as principles that express logical properties of sentences of the form ‘p is a reason for q’. Its main goal is to show how the theory of reasons outlined by Crupi and Iacona, which is based on their evidential account of conditionals, yields a formal treatment of such sentences that validates a restricted
-
From Contact Relations to Modal Operators, and Back Stud. Log. (IF 0.7) Pub Date : 2023-04-26 Rafał Gruszczyński, Paula Menchón
One of the standard axioms for Boolean contact algebras says that if a region x is in contact with the join of y and z, then x is in contact with at least one of the two regions. Our intention is to examine a stronger version of this axiom according to which if x is in contact with the supremum of some family S of regions, then there is a y in S that is in contact with x. We study a modal possibility
-
Some Observations on the FGH Theorem Stud. Log. (IF 0.7) Pub Date : 2023-04-26 Taishi Kurahashi
We investigate the Friedman–Goldfarb–Harrington theorem from two perspectives. Firstly, in the frameworks of classical and modal propositional logics, we study the forms of sentences whose existence is guaranteed by the FGH theorem. Secondly, we prove some variations of the FGH theorem with respect to Rosser provability predicates.
-
Semantics of Computable Physical Models Stud. Log. (IF 0.7) Pub Date : 2023-04-26 Matthew P. Szudzik
This article reformulates the theory of computable physical models, previously introduced by the author, as a branch of applied model theory in first-order logic. It provides a semantic approach to the philosophy of science that incorporates aspects of operationalism and Popper’s degrees of falsifiability.
-
Stalnakerian Connexive Logics Stud. Log. (IF 0.7) Pub Date : 2023-04-25 Xuefeng Wen
Motivated by supplying a new strategy for connexive logic and a better semantics for conditionals so that negating a conditional amounts to negating its consequent under the condition, we propose a new semantics for connexive conditional logic, by combining Kleene’s three-valued logic and a slight modification of Stalnaker’s semantics for conditionals. In the new semantics, selection functions for
-
Tense Operators on Distributive Lattices with Implication Stud. Log. (IF 0.7) Pub Date : 2023-04-25 Gustavo Pelaitay, William Zuluaga
Inspired by the definition of tense operators on distributive lattices presented by Chajda and Paseka in 2015, in this paper, we introduce and study the variety of tense distributive lattices with implication and we prove that these are categorically equivalent to a full subcategory of the category of tense centered Kleene algebras with implication. Moreover, we apply such an equivalence to describe
-
Williamson’s Abductive Case for the Material Conditional Account Stud. Log. (IF 0.7) Pub Date : 2023-04-15 Robert van Rooij, Karolina Krzyżanowska, Igor Douven
In Suppose and Tell, Williamson makes a new and original attempt to defend the material conditional account of indicative conditionals. His overarching argument is that this account offers the best explanation of the data concerning how people evaluate and use such conditionals. We argue that Williamson overlooks several important alternative explanations, some of which appear to explain the relevant
-
A First-Order Expansion of Artemov and Protopopescu’s Intuitionistic Epistemic Logic Stud. Log. (IF 0.7) Pub Date : 2023-03-20 Youan Su, Katsuhiko Sano
Intuitionistic epistemic logic by Artemov and Protopopescu (Rev Symb Log 9:266–298, 2016) accepts the axiom “if A, then A is known” (written \(A \supset K A\)) in terms of the Brouwer–Heyting–Kolmogorov interpretation. There are two variants of intuitionistic epistemic logic: one with the axiom “\(KA \supset \lnot \lnot A\)” and one without it. The former is called \(\textbf{IEL}\), and the latter
-
Birkhoff’s and Mal’cev’s Theorems for Implicational Tonoid Logics Stud. Log. (IF 0.7) Pub Date : 2023-01-31 Eunsuk Yang
In the context of implicational tonoid logics, this paper investigates analogues of Birkhoff’s two theorems, the so-called subdirect representation and varieties theorems, and of Mal’cev’s quasi-varieties 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