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  1. The Integral Construct of Science.Joseph Krecz - manuscript
    A number of general theories of physics provide a model for the fundamental rules that govern our universe, becoming a structural framework to which the new discoveries must conform. The theory of relativity is such a general theory. The theory of relativity is a complex theoretical framework that facilitates the understanding of the universal laws of physics. It is based on the curved space-time continuum fabric abstract concept, and it is well suited for interpreting cosmic events. More so, a general (...)
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  2. Not much higher-order vagueness in Williamson’s ’logic of clarity’.Nasim Mahoozi & Thomas Mormann - manuscript
    This paper deals with higher-order vagueness in Williamson's 'logic of clarity'. Its aim is to prove that for 'fixed margin models' (W,d,α ,[ ]) the notion of higher-order vagueness collapses to second-order vagueness. First, it is shown that fixed margin models can be reformulated in terms of similarity structures (W,~). The relation ~ is assumed to be reflexive and symmetric, but not necessarily transitive. Then, it is shown that the structures (W,~) come along with naturally defined maps h and s (...)
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  3. Qualia Logic.Paul Merriam - manuscript
    The logic of qualia is different than classical logic. We take the first steps in defining it and applying it to the Hard Problem.
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  4. M. Abad Varieties of Three-valued.A. M. Suardiaz A. Quantifier - forthcoming - Studia Logica.
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  5. Towards World Identification in Description Logics.Farshad Badie - forthcoming - Logical Investigations:115–134.
    Logical analysis of the applicability of nominals (which are introduced by hybrid logic) in the formal descriptions of the world (within modern knowledge representation and semantics-based systems) is very important because nominals, as second sorts of propositional symbols, can support logical identification of the described world at specific [temporal and/or spacial] states. This paper will focus on answering the philosophical-logical question of ‘how a fundamental world description in description logic (DL) and a nominal can be related to each other?’. Based (...)
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  6. Logical Characterisation of Possibilistic and Probabilistic Descriptions of Events in Description Logics.Farshad Badie - forthcoming - Bulletin of the Section of Logic.
    Description Logics (DLs) are a family of formal knowledge representation formalisms and the most well-known formalisms in semantics-based systems. The central focus of this research is on logical-terminological characterisation/analysis of possibilistic and probabilistic descriptions of events in DLs. Based on a logical characterisation of the concept of `being', this paper conceptualises events within DLs world descriptions. Accordingly, it deals with the concepts of `possibility of events' and `probability of events'. The main goal of this research is to investigate how possible (...)
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  7. An Occurrence Description Logic.Farshad Badie & Hans Götzsche - forthcoming - Logical Investigations:142-156.
    Description Logics (DLs) are a family of well-known terminological knowledge representation formalisms in modern semantics-based systems. This research focuses on analysing how our developed Occurrence Logic (OccL) can conceptually and logically support the development of a description logic. OccL is integrated into the alternative theory of natural language syntax in `Deviational Syntactic Structures' under the label `EFA(X)3' (or the third version of Epi-Formal Analysis in Syntax, EFA(X), which is a radical linguistic theory). From the logical point of view, OccL is (...)
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  8. Games and cardinalities in inquisitive first-order logic.Ivano Ciardelli & Gianluca Grilletti - forthcoming - Review of Symbolic Logic:1-28.
    Inquisitive first-order logic, InqBQ, is a system which extends classical first-order logic with formulas expressing questions. From a mathematical point of view, formulas in this logic express properties of sets of relational structures. This paper makes two contributions to the study of this logic. First, we describe an Ehrenfeucht–Fraïssé game for InqBQ and show that it characterizes the distinguishing power of the logic. Second, we use the game to study cardinality quantifiers in the inquisitive setting. That is, we study what (...)
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  9. Aristotelian diagrams for semantic and syntactic consequence.Lorenz Demey - forthcoming - Synthese:1-21.
    Several authors have recently studied Aristotelian diagrams for various metatheoretical notions from logic, such as tautology, satisfiability, and the Aristotelian relations themselves. However, all these metalogical Aristotelian diagrams focus on the semantic perspective on logical consequence, thus ignoring the complementary, and equally important, syntactic perspective. In this paper, I propose an explanation for this discrepancy, by arguing that the metalogical square of opposition for semantic consequence exhibits a natural analogy to the well-known square of opposition for the categorical statements from (...)
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  10. Abstract rationality: the 'logical' structure of attitudes.Franz Dietrich, Antonios Staras & Robert Sugden - forthcoming - Economics and Philosophy.
    We present an abstract model of rationality that focuses on structural properties of attitudes. Rationality requires coherence between your attitudes, such as your beliefs, values, and intentions. We define three 'logical' conditions on attitudes: consistency, completeness, and closedness. They parallel the familiar logical conditions on beliefs, but contrast with standard rationality conditions like preference transitivity. We establish a formal correspondence between our logical conditions and standard rationality conditions. Addressing John Broome's programme 'rationality through reasoning', we formally characterize how you can (...)
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  11. Explaining Experience In Nature: The Foundations Of Logic And Apprehension.Steven Ericsson-Zenith - forthcoming - Institute for Advanced Science & Engineering.
    At its core this book is concerned with logic and computation with respect to the mathematical characterization of sentient biophysical structure and its behavior. -/- Three related theories are presented: The first of these provides an explanation of how sentient individuals come to be in the world. The second describes how these individuals operate. And the third proposes a method for reasoning about the behavior of individuals in groups. -/- These theories are based upon a new explanation of experience in (...)
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  12. The Simplest Low Linear Order with No Computable Copies.Andrey Frolov & Maxim Zubkov - forthcoming - Journal of Symbolic Logic:1-15.
    A low linear order with no computable copy constructed by C. Jockusch and R. Soare has Hausdorff rank equal to $2$. In this regard, the question arises, how simple can be a low linear order with no computable copy from the point of view of the linear order type? The main result of this work is an example of a low strong $\eta $ -representation with no computable copy that is the simplest possible example.
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  13. Self-reference upfront: A study of self-referential gödel numberings.Balthasar Grabmayr & Albert Visser - forthcoming - Review of Symbolic Logic:1-40.
    In this paper we examine various requirements on the formalisation choices under which self-reference can be adequately formalised in arithmetic. In particular, we study self-referential numberings, which immediately provide a strong notion of self-reference even for expressively weak languages. The results of this paper suggest that the question whether truly self-referential reasoning can be formalised in arithmetic is more sensitive to the underlying coding apparatus than usually believed. As a case study, we show how this sensitivity affects the formal study (...)
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  14. Compatibility, compossibility, and epistemic modality.Wesley Holliday & Matthew Mandelkern - forthcoming - Proceedings of the 23rd Amsterdam Colloquium.
    We give a theory of epistemic modals in the framework of possibility semantics and axiomatize the corresponding logic, arguing that it aptly characterizes the ways in which reasoning with epistemic modals does, and does not, diverge from classical modal logic.
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  15. The bounds of transcendental logic. [REVIEW]S. Kovač - forthcoming - History and Philosophy of Logic:1-4.
  16. How Strong is Ramsey’s Theorem If Infinity Can Be Weak?Leszek Aleksander Kołodziejczyk, Katarzyna W. Kowalik & Keita Yokoyama - forthcoming - Journal of Symbolic Logic:1-20.
    We study the first-order consequences of Ramsey’s Theorem for k-colourings of n-tuples, for fixed $n, k \ge 2$, over the relatively weak second-order arithmetic theory $\mathrm {RCA}^*_0$. Using the Chong–Mourad coding lemma, we show that in a model of $\mathrm {RCA}^*_0$ that does not satisfy $\Sigma ^0_1$ induction, $\mathrm {RT}^n_k$ is equivalent to its relativization to any proper $\Sigma ^0_1$ -definable cut, so its truth value remains unchanged in all extensions of the model with the same first-order universe. We give (...)
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  17. Tractarian Logicism: Operations, Numbers, Induction.Gregory Landini - forthcoming - Review of Symbolic Logic:1-41.
  18. A note on the sequent calculi.Franco Parlamento & Flavio Previale - forthcoming - Review of Symbolic Logic:1-15.
    We show that the replacement rule of the sequent calculi ${\bf G3[mic]}^= $ in [8] can be replaced by the simpler rule in which one of the principal formulae is not repeated in the premiss.
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  19. Dialogue Games for Minimal Logic.Alexandra Pavlova - forthcoming - Logic and Logical Philosophy:1.
    In this paper, we define a class of dialogue games for Johansson’s minimal logic and prove that it corresponds to the validity of minimal logic. Many authors have stated similar results for intuitionistic and classical logic either with or without actually proving the correspondence. Rahman, Clerbout and Keiff [17] have already specified dialogues for minimal logic; however, they transformed it into Fitch-style natural deduction only. We propose a different specification for minimal logic with the proof of correspondence between the existence (...)
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  20. Abstract Forms of Quantification in the Quantified Argument Calculus.Edi Pavlović & Norbert Gratzl - forthcoming - Review of Symbolic Logic:1-32.
    The Quantified argument calculus (Quarc) has received a lot of attention recently as an interesting system of quantified logic which eschews the use of variables and unrestricted quantification, but nonetheless achieves results similar to the Predicate calculus (PC) by employing quantifiers applied directly to predicates instead. Despite this noted similarity, the issue of the relationship between Quarc and PC has so far not been definitively resolved. We address this question in the present paper, and then expand upon that result. Utilizing (...)
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  21. 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. [REVIEW]Ivo Pezlar - forthcoming - Studia Logica:1-4.
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  22. The lattice of super-Belnap logics.Adam Přenosil - forthcoming - Review of Symbolic Logic:1-50.
  23. The Ontological Innocence of Schematic Logic.Oliver William Tatton-Brown - forthcoming - Logic and Logical Philosophy:1.
    This paper gives a semantics for schematic logic, proving soundness and completeness. The argument for soundness is carried out in ontologically innocent fashion, relying only on the existence of formulae which are actually written down in the course of a derivation in the logic. This makes the logic available to a nominalist, even a nominalist who does not wish to rely on modal notions, and who accepts the possibility that the universe may in fact be finite.
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  24. Arbitrary Public Announcement Logic with Memory.Alexandru Baltag, Aybüke Özgün & Ana Lucia Vargas Sandoval - 2023 - Journal of Philosophical Logic 52 (1):53-110.
    We introduce Arbitrary Public Announcement Logic with Memory (APALM), obtained by adding to the models a ‘memory’ of the initial states, representing the information before any communication took place (“the prior”), and adding to the syntax operators that can access this memory. We show that APALM is recursively axiomatizable (in contrast to the original Arbitrary Public Announcement Logic, for which the corresponding question is still open). We present a complete recursive axiomatization, that includes a natural finitary rule, and study this (...)
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  25. Bounded-depth Frege complexity of Tseitin formulas for all graphs.Nicola Galesi, Dmitry Itsykson, Artur Riazanov & Anastasia Sofronova - 2023 - Annals of Pure and Applied Logic 174 (1):103166.
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  26. Valuation Semantics for First-Order Logics of Evidence and Truth.H. Antunes, A. Rodrigues, W. Carnielli & M. E. Coniglio - 2022 - Journal of Philosophical Logic 51 (5):1141-1173.
    This paper introduces the logic _Q__L__E__T_ _F_, a quantified extension of the logic of evidence and truth _L__E__T_ _F_, together with a corresponding sound and complete first-order non-deterministic valuation semantics. _L__E__T_ _F_ is a paraconsistent and paracomplete sentential logic that extends the logic of first-degree entailment (_FDE_) with a classicality operator ∘ and a non-classicality operator ∙, dual to each other: while ∘_A_ entails that _A_ behaves classically, ∙_A_ follows from _A_’s violating some classically valid inferences. The semantics of _Q__L__E__T_ (...)
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  27. On the Universality of Atomic and Molecular Logics via Protologics.Guillaume Aucher - 2022 - Logica Universalis 16 (1):285-322.
    After observing that the truth conditions of connectives of non–classical logics are generally defined in terms of formulas of first–order logic, we introduce ‘protologics’, a class of logics whose connectives are defined by arbitrary first–order formulas. Then, we introduce atomic and molecular logics, which are two subclasses of protologics that generalize our gaggle logics and which behave particularly well from a theoretical point of view. We also study and introduce a notion of equi-expressivity between two logics based on different classes (...)
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  28. Paraconsistent Metatheory: New Proofs with Old Tools.Guillermo Badia, Zach Weber & Patrick Girard - 2022 - Journal of Philosophical Logic 51 (4):825-856.
    This paper is a step toward showing what is achievable using non-classical metatheory—particularly, a substructural paraconsistent framework. What standard results, or analogues thereof, from the classical metatheory of first order logic can be obtained? We reconstruct some of the originals proofs for Completeness, Löwenheim-Skolem and Compactness theorems in the context of a substructural logic with the naive comprehension schema. The main result is that paraconsistent metatheory can ‘re-capture’ versions of standard theorems, given suitable restrictions and background assumptions; but the shift (...)
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  29. An Abductive Question-Answer System for the Minimal Logic of Formal Inconsistency $$\mathsf {mbC}$$ mbC.Szymon Chlebowski, Andrzej Gajda & Mariusz Urbański - 2022 - Studia Logica 110 (2):479-509.
    The aim in this paper is to define an Abductive Question-Answer System for the minimal logic of formal inconsistency \. As a proof-theoretical basis we employ the Socratic proofs method. The system produces abductive hypotheses; these are answers to abductive questions concerning derivability of formulas from sets of formulas. We integrated the generation of and the evaluation of hypotheses via constraints of consistency and significance being imposed on the system rules.
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  30. Priority merge and intersection modalities.Zoé Christoff, Norbert Gratzl & Olivier Roy - 2022 - Review of Symbolic Logic 15 (1):165-196.
    We study the logic of so-called lexicographic or priority merge for multi-agent plausibility models. We start with a systematic comparison between the logical behavior of priority merge and the more standard notion of pooling through intersection, used to define, for instance, distributed knowledge. We then provide a sound and complete axiomatization of the logic of priority merge, as well as a proof theory in labeled sequents that admits cut. We finally study Moorean phenomena and define a dynamic resolution operator for (...)
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  31. Coherence in inquisitive first-order logic.Ivano Ciardelli & Gianluca Grilletti - 2022 - Annals of Pure and Applied Logic 173 (9):103155.
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  32. Sequent-Calculi for Metainferential Logics.Bruno Da Ré & Federico Pailos - 2022 - Studia Logica 110 (2):319-353.
    In recent years, some theorists have argued that the clogics are not only defined by their inferences, but also by their metainferences. In this sense, logics that coincide in their inferences, but not in their metainferences were considered to be different. In this vein, some metainferential logics have been developed, as logics with metainferences of any level, built as hierarchies over known logics, such as \, and \. What is distinctive of these metainferential logics is that they are mixed, i.e. (...)
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  33. Derivability and Metainferential Validity.Bruno Da Ré, Damian Szmuc & Paula Teijeiro - 2022 - Journal of Philosophical Logic 51 (6):1521-1547.
    The aim of this article is to study the notion of derivability and its semantic counterpart in the context of non-transitive and non-reflexive substructural logics. For this purpose we focus on the study cases of the logics _S__T_ and _T__S_. In this respect, we show that this notion doesn’t coincide, in general, with a nowadays broadly used semantic approach towards metainferential validity: the notion of local validity. Following this, and building on some previous work by Humberstone, we prove that in (...)
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  34. A Probabilistic Logic Between $$LPP1$$ L P P 1 and $$LPP2$$ L P P 2.Šejla Dautović - 2022 - Logica Universalis 16 (1):323-333.
    An extension of the propositional probability logic \ given in Ognjanović et al. that allows mixing of propositional formulas and probabilistic formulas is introduced. We describe the corresponding class of models, and we show that the problem of deciding satisfiability is in NP. We provide infinitary axiomatization for the logic and we prove that the axiomatization is sound and strongly complete.
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  35. A Probabilistic Logic Between $$LPP1$$ L P P 1 and $$LPP2$$ L P P 2.Šejla Dautović - 2022 - Logica Universalis 16 (1-2):323-333.
    An extension of the propositional probability logic \ given in Ognjanović et al. that allows mixing of propositional formulas and probabilistic formulas is introduced. We describe the corresponding class of models, and we show that the problem of deciding satisfiability is in NP. We provide infinitary axiomatization for the logic and we prove that the axiomatization is sound and strongly complete.
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  36. A Unified Logic for Contingency and Accident.Jie Fan - 2022 - Journal of Philosophical Logic 51 (4):693-720.
    As shown in Fan, there are some similarities/resemblances between contingency and accident. Given this, one may naturally ask if we can unify the two operators to manifest all of their similarities/resemblances. In this article, instead of looking at the interactions between the two operators like in Fan, we turn our attention to the resemblances between the two operators. We extend the unification method in Fan to the current setting. The main results include some model-theoretical ones, such as expressivity, frame definability, (...)
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  37. Deep ST.Thomas M. Ferguson & Elisángela Ramírez-Cámara - 2022 - Journal of Philosophical Logic 51 (6):1261-1293.
    Many analyses of notion of _metainferences_ in the non-transitive logic ST have tackled the question of whether ST can be identified with classical logic. In this paper, we argue that the primary analyses are overly restrictive of the notion of metainference. We offer a more elegant and tractable semantics for the strict-tolerant hierarchy based on the three-valued function for the LP material conditional. This semantics can be shown to easily handle the introduction of _mixed_ inferences, _i.e._, inferences involving objects belonging (...)
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  38. From Truth Degree Comparison Games to Sequents-of-Relations Calculi for Gödel Logic.Christian Fermüller, Timo Lang & Alexandra Pavlova - 2022 - Logica Universalis 16 (1):221-235.
    We introduce a game for Gödel logic where the players’ interaction stepwise reduces claims about the relative order of truth degrees of complex formulas to atomic truth comparison claims. Using the concept of disjunctive game states this semantic game is lifted to a provability game, where winning strategies correspond to proofs in a sequents-of-relations calculus.
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  39. On Blass Translation for Leśniewski’s Propositional Ontology and Modal Logics.Takao Inoué - 2022 - Studia Logica 110 (1):265-289.
    In this paper, we shall give another proof of the faithfulness of Blass translation of the propositional fragment \ of Leśniewski’s ontology in the modal logic \ by means of Hintikka formula. And we extend the result to von Wright-type deontic logics, i.e., ten Smiley-Hanson systems of monadic deontic logic. As a result of observing the proofs we shall give general theorems on the faithfulness of B-translation with respect to normal modal logics complete to certain sets of well-known accessibility relations (...)
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  40. Infinitary action logic with exponentiation.Stepan L. Kuznetsov & Stanislav O. Speranski - 2022 - Annals of Pure and Applied Logic 173 (2):103057.
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  41. Rewriting the History of Connexive Logic.Wolfgang Lenzen - 2022 - Journal of Philosophical Logic 51 (3):525-553.
    The “official” history of connexive logic was written in 2012 by Storrs McCall who argued that connexive logic was founded by ancient logicians like Aristotle, Chrysippus, and Boethius; that it was further developed by medieval logicians like Abelard, Kilwardby, and Paul of Venice; and that it was rediscovered in the 19th and twentieth century by Lewis Carroll, Hugh MacColl, Frank P. Ramsey, and Everett J. Nelson. From 1960 onwards, connexive logic was finally transformed into non-classical calculi which partly concur with (...)
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  42. Investigations of isotropy and homogeneity of spacetime in first-order logic.Judit X. Madarász, Mike Stannett & Gergely Székely - 2022 - Annals of Pure and Applied Logic 173 (9):103153.
  43. On Logics and Semantics for Interpretability.Luka Mikec - 2022 - Bulletin of Symbolic Logic 28 (2):265-265.
  44. On existential definitions of c.e. subsets of rings of functions of characteristic 0.Russell Miller & Alexandra Shlapentokh - 2022 - Annals of Pure and Applied Logic 173 (4):103076.
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  45. Logic and African philosophy: seminal essays on African systems of thought: J. Chimakonam, editor. Delaware, Vernon Press, 2020, xiv + 326 pp., 16 plts, €48, ISBN: 978-1-62273-882-3. [REVIEW]E. Ofuasia - 2022 - History and Philosophy of Logic 43 (3):303-305.
    Logic and African Philosophy: Seminal Essays on African Systems of Thought is an edited work by Jonathan Chimakonam who is affiliated to the Philosophy Department at the University of Pretoria, Sou...
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  46. Paraconsistent Logic Programming in Three and Four-Valued Logics.Kleidson Êglicio Carvalho da Silva Oliveira - 2022 - Bulletin of Symbolic Logic 28 (2):260-260.
  47. Empty Logics.Federico Pailos - 2022 - Journal of Philosophical Logic 51 (6):1387-1415.
    _T__S_ is a logic that has no valid inferences. But, could there be a logic without valid metainferences? We will introduce _T__S_ _ω_, a logic without metainferential validities. Notwithstanding, _T__S_ _ω_ is not as empty—i.e., uninformative—as it gets, because it has many antivalidities. We will later introduce the two-standard logic [_T__S_ _ω_, _S__T_ _ω_ ], a logic without validities and antivalidities. Nevertheless, [_T__S_ _ω_, _S__T_ _ω_ ] is still informative, because it has many contingencies. The three-standard logic [ \(\mathbf {TS}_{\omega (...)
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  48. From Semantic Games to Provability: The Case of Gödel Logic.Alexandra Pavlova, Robert Freiman & Timo Lang - 2022 - Studia Logica 110 (2):429-456.
    We present a semantic game for Gödel logic and its extensions, where the players’ interaction stepwise reduces arbitrary claims about the relative order of truth degrees of complex formulas to atomic ones. The paper builds on a previously developed game for Gödel logic with projection operator in Fermüller et al., Information processing and management of uncertainty in knowledge-based systems, Springer, Cham, 2020, pp. 257–270). This game is extended to cover Gödel logic with involutive negations and constants, and then lifted to (...)
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  49. Supervaluations and the Strict-Tolerant Hierarchy.Brian Porter - 2022 - Journal of Philosophical Logic 51 (6):1367-1386.
    In a recent paper, Barrio, Pailos and Szmuc (BPS) show that there are logics that have exactly the validities of classical logic up to arbitrarily high levels of inference. They suggest that a logic therefore must be identified by its valid inferences at every inferential level. However, Scambler shows that there are logics with all the validities of classical logic at every inferential level, but with no antivalidities at any inferential level. Scambler concludes that in order to identify a logic, (...)
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  50. First-order Logics of Evidence and Truth with Constant and Variable Domains.Abilio Rodrigues & Henrique Antunes - 2022 - Logica Universalis 16 (3):419-449.
    The main aim of this paper is to introduce first-order versions of logics of evidence and truth, together with corresponding sound and complete Kripke semantics with variable and constant domains. According to the intuitive interpretation proposed here, these logics intend to represent possibly inconsistent and incomplete information bases over time. The paper also discusses the connections between Belnap-Dunn’s and da Costa’s approaches to paraconsistency, and argues that the logics of evidence and truth combine them in a very natural way.
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1 — 50 / 430