# Logic and Philosophy of Logic

Edited by Aleksandra Samonek (Université Catholique de Louvain, Jagiellonian University)
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1. Logics From Ultrafilters.Daniele Mundici - forthcoming - Review of Symbolic Logic:1-16.
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 Logics Classical Logic Deontic Logic Epistemic Logic Erotetic Logic Higher-Order Logic Modal and Intensional Logic Nonclassical Logics Temporal Logic Logics, Misc Logical Consequence and Entailment Logical Expressions Logical Constants Logical Connectives Quantifiers Variables Paradoxes Epistemic Paradoxes Liar Paradox Russell's Paradox Sorites Paradox Probabilistic Puzzles Decision-Theoretic Puzzles Paradoxes, Misc Logical Semantics and Logical Truth History of Logic Ancient Greek and Roman Logic Aristotelian Logic Buddhist Logic Indian Logic Medieval Logic 20th Century Logic 19th Century Logic History of Logic, Misc 17th/18th Century Logic Logic and Phil of Logic, Miscellaneous Dialetheism Epistemology of Logic Informal Logic Logical Expressivism Logical Pluralism Logic and Information Logic in Phil Model Theory Proof Theory Set Theory Mathematical Logic Introductions to Logic Logic and Phil of Logic, General Works Logic and Phil of Logic, Misc

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2. The Implicative Conditional.Eric Raidl & Gilberto Gomes - forthcoming - Journal of Philosophical Logic:1-47.
This paper investigates the implicative conditional, a connective intended to describe the logical behavior of an empirically defined class of natural language conditionals, also named implicative conditionals, which excludes concessive and some other conditionals. The implicative conditional strengthens the strict conditional with the possibility of the antecedent and of the contradictory of the consequent. $${p\Rightarrow q}$$ p ⇒ q is thus defined as $${\lnot } \Diamond {(p \wedge \lnot q) \wedge } \Diamond {p \wedge } \Diamond {\lnot q}$$ ¬ ◊ (...)
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 Logics Classical Logic Deontic Logic Epistemic Logic Erotetic Logic Higher-Order Logic Modal and Intensional Logic Nonclassical Logics Temporal Logic Logics, Misc Logical Consequence and Entailment Logical Expressions Logical Constants Logical Connectives Quantifiers Variables Paradoxes Epistemic Paradoxes Liar Paradox Russell's Paradox Sorites Paradox Probabilistic Puzzles Decision-Theoretic Puzzles Paradoxes, Misc Logical Semantics and Logical Truth History of Logic Ancient Greek and Roman Logic Aristotelian Logic Buddhist Logic Indian Logic Medieval Logic 20th Century Logic 19th Century Logic History of Logic, Misc 17th/18th Century Logic Logic and Phil of Logic, Miscellaneous Dialetheism Epistemology of Logic Informal Logic Logical Expressivism Logical Pluralism Logic and Information Logic in Phil Model Theory Proof Theory Set Theory Mathematical Logic Introductions to Logic Logic and Phil of Logic, General Works Logic and Phil of Logic, Misc

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3. Modal Information Logics: Axiomatizations and Decidability.Søren Brinck Knudstorp - 2023 - Journal of Philosophical Logic 52 (6):1723-1766.
The present paper studies formal properties of so-called modal information logics (MILs)—modal logics first proposed in (van Benthem 1996 ) as a way of using possible-worlds semantics to model a theory of information. They do so by extending the language of propositional logic with a binary modality defined in terms of being the supremum of two states. First proposed in 1996, MILs have been around for some time, yet not much is known: (van Benthem 2017, 2019 ) pose two central (...)
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 Logics Classical Logic Deontic Logic Epistemic Logic Erotetic Logic Higher-Order Logic Modal and Intensional Logic Nonclassical Logics Temporal Logic Logics, Misc Logical Consequence and Entailment Logical Expressions Logical Constants Logical Connectives Quantifiers Variables Paradoxes Epistemic Paradoxes Liar Paradox Russell's Paradox Sorites Paradox Probabilistic Puzzles Decision-Theoretic Puzzles Paradoxes, Misc Logical Semantics and Logical Truth History of Logic Ancient Greek and Roman Logic Aristotelian Logic Buddhist Logic Indian Logic Medieval Logic 20th Century Logic 19th Century Logic History of Logic, Misc 17th/18th Century Logic Logic and Phil of Logic, Miscellaneous Dialetheism Epistemology of Logic Informal Logic Logical Expressivism Logical Pluralism Logic and Information Logic in Phil Model Theory Proof Theory Set Theory Mathematical Logic Introductions to Logic Logic and Phil of Logic, General Works Logic and Phil of Logic, Misc

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4. Truth Meets Vagueness. Unifying the Semantic and the Soritical Paradoxes.Riccardo Bruni & Lorenzo Rossi - 2023 - Journal of Philosophical Logic 52 (6):1637-1671.
Semantic and soritical paradoxes display remarkable family resemblances. For one thing, several non-classical logics have been independently applied to both kinds of paradoxes. For another, revenge paradoxes and higher-order vagueness—among the most serious problems targeting solutions to semantic and soritical paradoxes—exhibit a rather similar dynamics. Some authors have taken these facts to suggest that truth and vagueness require a unified logical framework, or perhaps that the truth predicate is itself vague. However, a common core of semantic and soritical paradoxes has (...)
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 Logics Classical Logic Deontic Logic Epistemic Logic Erotetic Logic Higher-Order Logic Modal and Intensional Logic Nonclassical Logics Temporal Logic Logics, Misc Logical Consequence and Entailment Logical Expressions Logical Constants Logical Connectives Quantifiers Variables Paradoxes Epistemic Paradoxes Liar Paradox Russell's Paradox Sorites Paradox Probabilistic Puzzles Decision-Theoretic Puzzles Paradoxes, Misc Logical Semantics and Logical Truth History of Logic Ancient Greek and Roman Logic Aristotelian Logic Buddhist Logic Indian Logic Medieval Logic 20th Century Logic 19th Century Logic History of Logic, Misc 17th/18th Century Logic Logic and Phil of Logic, Miscellaneous Dialetheism Epistemology of Logic Informal Logic Logical Expressivism Logical Pluralism Logic and Information Logic in Phil Model Theory Proof Theory Set Theory Mathematical Logic Introductions to Logic Logic and Phil of Logic, General Works Logic and Phil of Logic, Misc

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5. A Basis for AGM Revision in Bayesian Probability Revision.Sven Ove Hansson - 2023 - Journal of Philosophical Logic 52 (6):1535-1559.
In standard Bayesian probability revision, the adoption of full beliefs (propositions with probability 1) is irreversible. Once an agent has full belief in a proposition, no subsequent revision can remove that belief. This is an unrealistic feature, and it also makes probability revision incompatible with belief change theory, which focuses on how the set of full beliefs is modified through both additions and retractions. This problem in probability theory can be solved in a model that (i) lets the codomain of (...)
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 Logics Classical Logic Deontic Logic Epistemic Logic Erotetic Logic Higher-Order Logic Modal and Intensional Logic Nonclassical Logics Temporal Logic Logics, Misc Logical Consequence and Entailment Logical Expressions Logical Constants Logical Connectives Quantifiers Variables Paradoxes Epistemic Paradoxes Liar Paradox Russell's Paradox Sorites Paradox Probabilistic Puzzles Decision-Theoretic Puzzles Paradoxes, Misc Logical Semantics and Logical Truth History of Logic Ancient Greek and Roman Logic Aristotelian Logic Buddhist Logic Indian Logic Medieval Logic 20th Century Logic 19th Century Logic History of Logic, Misc 17th/18th Century Logic Logic and Phil of Logic, Miscellaneous Dialetheism Epistemology of Logic Informal Logic Logical Expressivism Logical Pluralism Logic and Information Logic in Phil Model Theory Proof Theory Set Theory Mathematical Logic Introductions to Logic Logic and Phil of Logic, General Works Logic and Phil of Logic, Misc

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6. Subject-Matter and Intensional Operators II: Applications to the Theory of Topic-Sensitive Intentional Modals.Thomas Macaulay Ferguson - 2023 - Journal of Philosophical Logic 52 (6):1673-1701.
In frameworks in which _topic-__theoretic_ considerations—_e.g._, tracking _subject-matter_ or _topic_—are given equal importance with _veridical_ considerations, assigning topics to formulae in a satisfactory way is of critical importance. While intuitions are more-or-less solid for _extensional_ formulae in a propositional language, arriving at a compelling account of the subject-matter of _intensional_ formulae, _i.e._, formulae including intensional operators, is more challenging. This paper continues previous work on modeling topics of intensional formulae in William Parry’s logic of analytic implication, adapting the general techniques (...)
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 Logics Classical Logic Deontic Logic Epistemic Logic Erotetic Logic Higher-Order Logic Modal and Intensional Logic Nonclassical Logics Temporal Logic Logics, Misc Logical Consequence and Entailment Logical Expressions Logical Constants Logical Connectives Quantifiers Variables Paradoxes Epistemic Paradoxes Liar Paradox Russell's Paradox Sorites Paradox Probabilistic Puzzles Decision-Theoretic Puzzles Paradoxes, Misc Logical Semantics and Logical Truth History of Logic Ancient Greek and Roman Logic Aristotelian Logic Buddhist Logic Indian Logic Medieval Logic 20th Century Logic 19th Century Logic History of Logic, Misc 17th/18th Century Logic Logic and Phil of Logic, Miscellaneous Dialetheism Epistemology of Logic Informal Logic Logical Expressivism Logical Pluralism Logic and Information Logic in Phil Model Theory Proof Theory Set Theory Mathematical Logic Introductions to Logic Logic and Phil of Logic, General Works Logic and Phil of Logic, Misc

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7. Two Examples Concerning Existential Undecidability in Fields.Philip Dittmann - forthcoming - Journal of Symbolic Logic:1-10.
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 Logics Classical Logic Deontic Logic Epistemic Logic Erotetic Logic Higher-Order Logic Modal and Intensional Logic Nonclassical Logics Temporal Logic Logics, Misc Logical Consequence and Entailment Logical Expressions Logical Constants Logical Connectives Quantifiers Variables Paradoxes Epistemic Paradoxes Liar Paradox Russell's Paradox Sorites Paradox Probabilistic Puzzles Decision-Theoretic Puzzles Paradoxes, Misc Logical Semantics and Logical Truth History of Logic Ancient Greek and Roman Logic Aristotelian Logic Buddhist Logic Indian Logic Medieval Logic 20th Century Logic 19th Century Logic History of Logic, Misc 17th/18th Century Logic Logic and Phil of Logic, Miscellaneous Dialetheism Epistemology of Logic Informal Logic Logical Expressivism Logical Pluralism Logic and Information Logic in Phil Model Theory Proof Theory Set Theory Mathematical Logic Introductions to Logic Logic and Phil of Logic, General Works Logic and Phil of Logic, Misc

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8. On the existence of strong proof complexity generators.Jan Krajíček - forthcoming - Bulletin of Symbolic Logic:1-22.
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 Logics Classical Logic Deontic Logic Epistemic Logic Erotetic Logic Higher-Order Logic Modal and Intensional Logic Nonclassical Logics Temporal Logic Logics, Misc Logical Consequence and Entailment Logical Expressions Logical Constants Logical Connectives Quantifiers Variables Paradoxes Epistemic Paradoxes Liar Paradox Russell's Paradox Sorites Paradox Probabilistic Puzzles Decision-Theoretic Puzzles Paradoxes, Misc Logical Semantics and Logical Truth History of Logic Ancient Greek and Roman Logic Aristotelian Logic Buddhist Logic Indian Logic Medieval Logic 20th Century Logic 19th Century Logic History of Logic, Misc 17th/18th Century Logic Logic and Phil of Logic, Miscellaneous Dialetheism Epistemology of Logic Informal Logic Logical Expressivism Logical Pluralism Logic and Information Logic in Phil Model Theory Proof Theory Set Theory Mathematical Logic Introductions to Logic Logic and Phil of Logic, General Works Logic and Phil of Logic, Misc

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9. Logic-Sensitivity and Bitstring Semantics in the Square of Opposition.Lorenz Demey & Stef Frijters - 2023 - Journal of Philosophical Logic 52 (6):1703-1721.
This paper explores the interplay between logic-sensitivity and bitstring semantics in the square of opposition. Bitstring semantics is a combinatorial technique for representing the formulas that appear in a logical diagram, while logic-sensitivity entails that such a diagram may depend, not only on the formulas involved, but also on the logic with respect to which they are interpreted. These two topics have already been studied extensively in logical geometry, and are thus well-understood by themselves. However, the precise details of their (...)
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 Logics Classical Logic Deontic Logic Epistemic Logic Erotetic Logic Higher-Order Logic Modal and Intensional Logic Nonclassical Logics Temporal Logic Logics, Misc Logical Consequence and Entailment Logical Expressions Logical Constants Logical Connectives Quantifiers Variables Paradoxes Epistemic Paradoxes Liar Paradox Russell's Paradox Sorites Paradox Probabilistic Puzzles Decision-Theoretic Puzzles Paradoxes, Misc Logical Semantics and Logical Truth History of Logic Ancient Greek and Roman Logic Aristotelian Logic Buddhist Logic Indian Logic Medieval Logic 20th Century Logic 19th Century Logic History of Logic, Misc 17th/18th Century Logic Logic and Phil of Logic, Miscellaneous Dialetheism Epistemology of Logic Informal Logic Logical Expressivism Logical Pluralism Logic and Information Logic in Phil Model Theory Proof Theory Set Theory Mathematical Logic Introductions to Logic Logic and Phil of Logic, General Works Logic and Phil of Logic, Misc

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10. Quantum Epistemology and Constructivism.Patrick Fraser, Nuriya Nurgalieva & Lídia del Rio - 2023 - Journal of Philosophical Logic 52 (6):1561-1574.
Constructivist epistemology posits that all truths are knowable. One might ask to what extent constructivism is compatible with naturalized epistemology and knowledge obtained from inference-making using successful scientific theories. If quantum theory correctly describes the structure of the physical world, and if quantum theoretic inferences about which measurement outcomes will be observed with unit probability count as knowledge, we demonstrate that constructivism cannot be upheld. Our derivation is compatible with both intuitionistic and quantum propositional logic. This result is implied by (...)
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 Logics Classical Logic Deontic Logic Epistemic Logic Erotetic Logic Higher-Order Logic Modal and Intensional Logic Nonclassical Logics Temporal Logic Logics, Misc Logical Consequence and Entailment Logical Expressions Logical Constants Logical Connectives Quantifiers Variables Paradoxes Epistemic Paradoxes Liar Paradox Russell's Paradox Sorites Paradox Probabilistic Puzzles Decision-Theoretic Puzzles Paradoxes, Misc Logical Semantics and Logical Truth History of Logic Ancient Greek and Roman Logic Aristotelian Logic Buddhist Logic Indian Logic Medieval Logic 20th Century Logic 19th Century Logic History of Logic, Misc 17th/18th Century Logic Logic and Phil of Logic, Miscellaneous Dialetheism Epistemology of Logic Informal Logic Logical Expressivism Logical Pluralism Logic and Information Logic in Phil Model Theory Proof Theory Set Theory Mathematical Logic Introductions to Logic Logic and Phil of Logic, General Works Logic and Phil of Logic, Misc

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11. Non-Tightness in Class Theory and Second-Order Arithmetic.Alfredo Roque Freire & Kameryn J. Williams - forthcoming - Journal of Symbolic Logic:1-28.
A theory T is tight if different deductively closed extensions of T (in the same language) cannot be bi-interpretable. Many well-studied foundational theories are tight, including $\mathsf {PA}$ [39], $\mathsf {ZF}$, $\mathsf {Z}_2$, and $\mathsf {KM}$ [6]. In this article we extend Enayat’s investigations to subsystems of these latter two theories. We prove that restricting the Comprehension schema of $\mathsf {Z}_2$ and $\mathsf {KM}$ gives non-tight theories. Specifically, we show that $\mathsf {GB}$ and $\mathsf {ACA}_0$ each admit different bi-interpretable extensions, (...)
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 Logics Classical Logic Deontic Logic Epistemic Logic Erotetic Logic Higher-Order Logic Modal and Intensional Logic Nonclassical Logics Temporal Logic Logics, Misc Logical Consequence and Entailment Logical Expressions Logical Constants Logical Connectives Quantifiers Variables Paradoxes Epistemic Paradoxes Liar Paradox Russell's Paradox Sorites Paradox Probabilistic Puzzles Decision-Theoretic Puzzles Paradoxes, Misc Logical Semantics and Logical Truth History of Logic Ancient Greek and Roman Logic Aristotelian Logic Buddhist Logic Indian Logic Medieval Logic 20th Century Logic 19th Century Logic History of Logic, Misc 17th/18th Century Logic Logic and Phil of Logic, Miscellaneous Dialetheism Epistemology of Logic Informal Logic Logical Expressivism Logical Pluralism Logic and Information Logic in Phil Model Theory Proof Theory Set Theory Mathematical Logic Introductions to Logic Logic and Phil of Logic, General Works Logic and Phil of Logic, Misc

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12. Ultralogic as Universal was drafted in 1976, appeared in 1977 as ‘Ultralogic as Universal?’ in The Relevance Logic Newsletter, 2 (1–2) and was reprinted as an appendix to Exploring Meinong’s Jungle...
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 Logics Classical Logic Deontic Logic Epistemic Logic Erotetic Logic Higher-Order Logic Modal and Intensional Logic Nonclassical Logics Temporal Logic Logics, Misc Logical Consequence and Entailment Logical Expressions Logical Constants Logical Connectives Quantifiers Variables Paradoxes Epistemic Paradoxes Liar Paradox Russell's Paradox Sorites Paradox Probabilistic Puzzles Decision-Theoretic Puzzles Paradoxes, Misc Logical Semantics and Logical Truth History of Logic Ancient Greek and Roman Logic Aristotelian Logic Buddhist Logic Indian Logic Medieval Logic 20th Century Logic 19th Century Logic History of Logic, Misc 17th/18th Century Logic Logic and Phil of Logic, Miscellaneous Dialetheism Epistemology of Logic Informal Logic Logical Expressivism Logical Pluralism Logic and Information Logic in Phil Model Theory Proof Theory Set Theory Mathematical Logic Introductions to Logic Logic and Phil of Logic, General Works Logic and Phil of Logic, Misc

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13. Order Types of Models of Fragments of Peano Arithmetic.Lorenzo Galeotti & Benedikt Löwe - 2022 - Bulletin of Symbolic Logic 28 (2):182-206.
The complete characterisation of order types of non-standard models of Peano arithmetic and its extensions is a famous open problem. In this paper, we consider subtheories of Peano arithmetic (both with and without induction), in particular, theories formulated in proper fragments of the full language of arithmetic. We study the order types of their non-standard models and separate all considered theories via their possible order types. We compare the theories with and without induction and observe that the theories without induction (...)
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 Logics Classical Logic Deontic Logic Epistemic Logic Erotetic Logic Higher-Order Logic Modal and Intensional Logic Nonclassical Logics Temporal Logic Logics, Misc Logical Consequence and Entailment Logical Expressions Logical Constants Logical Connectives Quantifiers Variables Paradoxes Epistemic Paradoxes Liar Paradox Russell's Paradox Sorites Paradox Probabilistic Puzzles Decision-Theoretic Puzzles Paradoxes, Misc Logical Semantics and Logical Truth History of Logic Ancient Greek and Roman Logic Aristotelian Logic Buddhist Logic Indian Logic Medieval Logic 20th Century Logic 19th Century Logic History of Logic, Misc 17th/18th Century Logic Logic and Phil of Logic, Miscellaneous Dialetheism Epistemology of Logic Informal Logic Logical Expressivism Logical Pluralism Logic and Information Logic in Phil Model Theory Proof Theory Set Theory Mathematical Logic Introductions to Logic Logic and Phil of Logic, General Works Logic and Phil of Logic, Misc

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14. On categorical structures arising from implicative algebras: from topology to assemblies.Samuele Maschio & Davide Trotta - forthcoming - Annals of Pure and Applied Logic.
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 Logics Classical Logic Deontic Logic Epistemic Logic Erotetic Logic Higher-Order Logic Modal and Intensional Logic Nonclassical Logics Temporal Logic Logics, Misc Logical Consequence and Entailment Logical Expressions Logical Constants Logical Connectives Quantifiers Variables Paradoxes Epistemic Paradoxes Liar Paradox Russell's Paradox Sorites Paradox Probabilistic Puzzles Decision-Theoretic Puzzles Paradoxes, Misc Logical Semantics and Logical Truth History of Logic Ancient Greek and Roman Logic Aristotelian Logic Buddhist Logic Indian Logic Medieval Logic 20th Century Logic 19th Century Logic History of Logic, Misc 17th/18th Century Logic Logic and Phil of Logic, Miscellaneous Dialetheism Epistemology of Logic Informal Logic Logical Expressivism Logical Pluralism Logic and Information Logic in Phil Model Theory Proof Theory Set Theory Mathematical Logic Introductions to Logic Logic and Phil of Logic, General Works Logic and Phil of Logic, Misc

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15. Outline of an Intensional Theory of Truth.Roy T. Cook - 2022 - Notre Dame Journal of Formal Logic 63 (1):81-108.
We expand on the fixed point semantic approach of Kripke via the addition of two unary intensional operators: a paradoxicality operator Π where Π(Φ) is true at a fixed point if and only if Φ is paradoxical (i.e., if and only if Φ receives the third, non-classical value on all fixed points that extend the current fixed point), and an unbounded truth operator Υ⊤ where Υ⊤(Φ) is true at a fixed point if and only if any fixed point extending the (...)
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 Logics Classical Logic Deontic Logic Epistemic Logic Erotetic Logic Higher-Order Logic Modal and Intensional Logic Nonclassical Logics Temporal Logic Logics, Misc Logical Consequence and Entailment Logical Expressions Logical Constants Logical Connectives Quantifiers Variables Paradoxes Epistemic Paradoxes Liar Paradox Russell's Paradox Sorites Paradox Probabilistic Puzzles Decision-Theoretic Puzzles Paradoxes, Misc Logical Semantics and Logical Truth History of Logic Ancient Greek and Roman Logic Aristotelian Logic Buddhist Logic Indian Logic Medieval Logic 20th Century Logic 19th Century Logic History of Logic, Misc 17th/18th Century Logic Logic and Phil of Logic, Miscellaneous Dialetheism Epistemology of Logic Informal Logic Logical Expressivism Logical Pluralism Logic and Information Logic in Phil Model Theory Proof Theory Set Theory Mathematical Logic Introductions to Logic Logic and Phil of Logic, General Works Logic and Phil of Logic, Misc

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16. La genèse des structures logiques élémentaires.Bärbel Inhelder - 1959 - Neuchâtel,: Delachaux & Niestlé. Edited by Jean Piaget.
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 Logics Classical Logic Deontic Logic Epistemic Logic Erotetic Logic Higher-Order Logic Modal and Intensional Logic Nonclassical Logics Temporal Logic Logics, Misc Logical Consequence and Entailment Logical Expressions Logical Constants Logical Connectives Quantifiers Variables Paradoxes Epistemic Paradoxes Liar Paradox Russell's Paradox Sorites Paradox Probabilistic Puzzles Decision-Theoretic Puzzles Paradoxes, Misc Logical Semantics and Logical Truth History of Logic Ancient Greek and Roman Logic Aristotelian Logic Buddhist Logic Indian Logic Medieval Logic 20th Century Logic 19th Century Logic History of Logic, Misc 17th/18th Century Logic Logic and Phil of Logic, Miscellaneous Dialetheism Epistemology of Logic Informal Logic Logical Expressivism Logical Pluralism Logic and Information Logic in Phil Model Theory Proof Theory Set Theory Mathematical Logic Introductions to Logic Logic and Phil of Logic, General Works Logic and Phil of Logic, Misc
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17. Unified Deductive Systems: An Outline.Alex Citkin - 2023 - Logica Universalis 17 (4):483-509.
Our goal is to develop a syntactical apparatus for propositional logics in which the accepted and rejected propositions have the same status and obeying treated in the same way. The suggested approach is based on the ideas of Łukasiewicz used for the classical logic and in addition, it includes the use of multiple conclusion rules. More precisely, a consequence relation is defined on a set of statements of forms “proposition _A_ is accepted” and “proposition _A_ is rejected”, where _A_ is (...)
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 Logics Classical Logic Deontic Logic Epistemic Logic Erotetic Logic Higher-Order Logic Modal and Intensional Logic Nonclassical Logics Temporal Logic Logics, Misc Logical Consequence and Entailment Logical Expressions Logical Constants Logical Connectives Quantifiers Variables Paradoxes Epistemic Paradoxes Liar Paradox Russell's Paradox Sorites Paradox Probabilistic Puzzles Decision-Theoretic Puzzles Paradoxes, Misc Logical Semantics and Logical Truth History of Logic Ancient Greek and Roman Logic Aristotelian Logic Buddhist Logic Indian Logic Medieval Logic 20th Century Logic 19th Century Logic History of Logic, Misc 17th/18th Century Logic Logic and Phil of Logic, Miscellaneous Dialetheism Epistemology of Logic Informal Logic Logical Expressivism Logical Pluralism Logic and Information Logic in Phil Model Theory Proof Theory Set Theory Mathematical Logic Introductions to Logic Logic and Phil of Logic, General Works Logic and Phil of Logic, Misc

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18. On Consequence and Rejection as Operators.Alexei Muravitsky - 2023 - Logica Universalis 17 (4):443-460.
This paper is devoted to the concepts of consequence and rejection, formulated as operators on a nonempty set of sentences, which may initially be unstructured. One of the issues that we pay attention to is the “cyclicity” of these concepts when they are defined one through the other. In addition, we explore this cyclicity, when the set of all sentences acquires some structure, or we can assume some structure of sentences in the sense that the operation of substitution can be (...)
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 Logics Classical Logic Deontic Logic Epistemic Logic Erotetic Logic Higher-Order Logic Modal and Intensional Logic Nonclassical Logics Temporal Logic Logics, Misc Logical Consequence and Entailment Logical Expressions Logical Constants Logical Connectives Quantifiers Variables Paradoxes Epistemic Paradoxes Liar Paradox Russell's Paradox Sorites Paradox Probabilistic Puzzles Decision-Theoretic Puzzles Paradoxes, Misc Logical Semantics and Logical Truth History of Logic Ancient Greek and Roman Logic Aristotelian Logic Buddhist Logic Indian Logic Medieval Logic 20th Century Logic 19th Century Logic History of Logic, Misc 17th/18th Century Logic Logic and Phil of Logic, Miscellaneous Dialetheism Epistemology of Logic Informal Logic Logical Expressivism Logical Pluralism Logic and Information Logic in Phil Model Theory Proof Theory Set Theory Mathematical Logic Introductions to Logic Logic and Phil of Logic, General Works Logic and Phil of Logic, Misc

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19. Rejection: A Historico-Epistemological View.Alexei Muravitsky - 2023 - Logica Universalis 17 (4):461-482.
We seek to trace how the assertion–rejection dichotomy arose, as well as in what forms it was realized in logical discourse. From this viewpoint, we observe the approaches to the concept of rejection by Łukasiewicz, Carnap, and Słupecki. We also explore the controversy between rejection and negation. Our main observation is that for a correct understanding of this dichotomy, it is necessary to distinguish between the object language and metalanguages of different levels.
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 Logics Classical Logic Deontic Logic Epistemic Logic Erotetic Logic Higher-Order Logic Modal and Intensional Logic Nonclassical Logics Temporal Logic Logics, Misc Logical Consequence and Entailment Logical Expressions Logical Constants Logical Connectives Quantifiers Variables Paradoxes Epistemic Paradoxes Liar Paradox Russell's Paradox Sorites Paradox Probabilistic Puzzles Decision-Theoretic Puzzles Paradoxes, Misc Logical Semantics and Logical Truth History of Logic Ancient Greek and Roman Logic Aristotelian Logic Buddhist Logic Indian Logic Medieval Logic 20th Century Logic 19th Century Logic History of Logic, Misc 17th/18th Century Logic Logic and Phil of Logic, Miscellaneous Dialetheism Epistemology of Logic Informal Logic Logical Expressivism Logical Pluralism Logic and Information Logic in Phil Model Theory Proof Theory Set Theory Mathematical Logic Introductions to Logic Logic and Phil of Logic, General Works Logic and Phil of Logic, Misc

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20. Operator Counterparts of Types of Reasoning.Urszula Wybraniec-Skardowska - 2023 - Logica Universalis 17 (4):511-528.
Logical and philosophical literature provides different classifications of reasoning. In the Polish literature on the subject, for instance, there are three popular ones accepted by representatives of the Lvov-Warsaw School: Jan Łukasiewicz, Tadeusz Czeżowski and Kazimierz Ajdukiewicz (Ajdukiewicz in Logika pragmatyczna [Pragmatic Logic]. PWN, Warsaw (1965, 2nd ed. 1974). Translated as: Pragmatic Logic. Reidel & PWN, Dordrecht, 1975). The author of this paper, having modified those classifications, distinguished the following types of reasoning: (1) deductive and (2) non-deductive, and additionally two (...)
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21. Preface to the Rejection Special Issue.Alex Citkin & Alexei Muravitsky - 2023 - Logica Universalis 17 (4):405-410.
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22. A Sound and Complete Tableaux Calculus for Reichenbach’s Quantum Mechanics Logic.Pablo Caballero & Pablo Valencia - forthcoming - Journal of Philosophical Logic:1-23.
In 1944 Hans Reichenbach developed a three-valued propositional logic (RQML) in order to account for certain causal anomalies in quantum mechanics. In this logic, the truth-value _indeterminate_ is assigned to those statements describing physical phenomena that cannot be understood in causal terms. However, Reichenbach did not develop a deductive calculus for this logic. The aim of this paper is to develop such a calculus by means of First Degree Entailment logic (FDE) and to prove it sound and complete with respect (...)
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23. Belief and Counterfactuals: A Study in Means-end Philosophy.G. Haas - forthcoming - History and Philosophy of Logic:1-2.
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24. On Pretabular Extensions of Relevance Logic.Asadollah Fallahi & James Gordon Raftery - forthcoming - Studia Logica:1-19.
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 $$(p\rightarrow q)\vee (q\rightarrow p)$$ ( p → q ) ∨ ( q → p ) has infinitely many pretabular axiomatic extensions, regardless of the presence or absence of Ackermann constants.
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25. Franz Huber’s book addresses beliefs and counterfactuals and their relationship. Using a normative approach, the author explores how agents should believe and change their beliefs, given they have...
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26. Morphisms Between Aristotelian Diagrams.Alexander De Klerck, Leander Vignero & Lorenz Demey - forthcoming - Logica Universalis:1-35.
In logical geometry, Aristotelian diagrams are studied in a precise and systematic way. Although there has recently been a good amount of progress in logical geometry, it is still unknown which underlying mathematical framework is best suited for formalizing the study of these diagrams. Hence, in this paper, the main aim is to formulate such a framework, using the powerful language of category theory. We build multiple categories, which all have Aristotelian diagrams as their objects, while having different kinds of (...)
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27. Finite Tree-Countermodels via Refutation Systems in Extensions of Positive Logic with Strong Negation.Tomasz Skura - 2023 - Logica Universalis 17 (4):433-441.
A sufficient condition for an extension of positive logic with strong negation to be characterized by a class of finite trees is given.
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28. Complementary Proof Nets for Classical Logic.Gabriele Pulcini & Achille C. Varzi - 2023 - Logica Universalis 17 (4):411-432.
A complementary system for a given logic is a proof system whose theorems are exactly the formulas that are not valid according to the logic in question. This article is a contribution to the complementary proof theory of classical propositional logic. In particular, we present a complementary proof-net system, $$\textsf{CPN}$$ CPN, that is sound and complete with respect to the set of all classically invalid (one-side) sequents. We also show that cut elimination in $$\textsf{CPN}$$ CPN enjoys strong normalization along with (...)
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29. A Generalization of Beall’s Off-Topic Interpretation.Yang Song, Hitoshi Omori, Jonas R. B. Arenhart & Satoshi Tojo - forthcoming - Studia Logica:1-40.
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 Beall’s interpretation, and offer an alternative semantic framework that reflects our motivations. Second, by making (...)
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30. A Logical Theory for Conditional Weak Ontic Necessity in Branching Time.Fengkui Ju - forthcoming - Studia Logica:1-34.
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 instant operator, the last instant operator, and the operator for conditional weak ontic necessity. Formulas (...)
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31. Modes of Convergence to the Truth: Steps Toward a Better Epistemology of Induction.L. I. N. Hanti - 2022 - Review of Symbolic Logic 15 (2):277-310.
Evaluative studies of inductive inferences have been pursued extensively with mathematical rigor in many disciplines, such as statistics, econometrics, computer science, and formal epistemology. Attempts have been made in those disciplines to justify many different kinds of inductive inferences, to varying extents. But somehow those disciplines have said almost nothing to justify a most familiar kind of induction, an example of which is this: “We’ve seen this many ravens and they all are black, so all ravens are black.” This is (...)
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32. On Model-Theoretic Connected Groups.Jakub Gismatullin - forthcoming - Journal of Symbolic Logic:1-25.
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33. Ontological Purity for Formal Proofs.Robin Martinot - forthcoming - Review of Symbolic Logic:1-44.
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34. Preservation of natp.Jinhoo Ahn, Joonhee Kim, Hyoyoon Lee & Junguk Lee - forthcoming - Journal of Mathematical Logic.
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35. 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 will be denoted by $$a\rightarrow b$$. The integral srl-monoids can be regarded as algebras $$(A,\wedge,\vee,\cdot,\rightarrow,1)$$ of type (2, 2, (...)
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 Logics Classical Logic Deontic Logic Epistemic Logic Erotetic Logic Higher-Order Logic Modal and Intensional Logic Nonclassical Logics Temporal Logic Logics, Misc Logical Consequence and Entailment Logical Expressions Logical Constants Logical Connectives Quantifiers Variables Paradoxes Epistemic Paradoxes Liar Paradox Russell's Paradox Sorites Paradox Probabilistic Puzzles Decision-Theoretic Puzzles Paradoxes, Misc Logical Semantics and Logical Truth History of Logic Ancient Greek and Roman Logic Aristotelian Logic Buddhist Logic Indian Logic Medieval Logic 20th Century Logic 19th Century Logic History of Logic, Misc 17th/18th Century Logic Logic and Phil of Logic, Miscellaneous Dialetheism Epistemology of Logic Informal Logic Logical Expressivism Logical Pluralism Logic and Information Logic in Phil Model Theory Proof Theory Set Theory Mathematical Logic Introductions to Logic Logic and Phil of Logic, General Works Logic and Phil of Logic, Misc

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36. Connexive Negation.Luis Estrada-González & Ricardo Arturo Nicolás-Francisco - forthcoming - Studia Logica:1-29.
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 properties to the negation to validate the theses. In this paper we examine that possibility, not sufficiently explored in (...)
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37. Logische Untersuchungen.Edmund Husserl - 1968 - Tübingen,: M. Niemeyer.
1. Bd. Prolegomena zur reinen Logik. - 2. Bd. 1. T. Untersuchungen zur Phänomenologie und Theorie der Erkenntnis. 2. T. Elemente einer phänomenologischen Aufklärung der Erkenntnis.
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38. Hyperintensionality and Fine-Grained Semantics.Aleksander Parol - 2023 - Studia Logica 111 (6):1083-1087.
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39. Systems for Non-Reflexive Consequence.Carlo Nicolai & Lorenzo Rossi - 2023 - Studia Logica 111 (6):947-977.
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 in our non-reflexive framework.
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40. The Elimination of Direct Self-reference.Qianli Zeng & Ming Hsiung - 2023 - Studia Logica 111 (6):1037-1055.
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 can preserve the primary periods of Boolean paradoxes: whenever _m_ is relatively prime to all primary periods of a Boolean paradox, this (...)
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 Logics Classical Logic Deontic Logic Epistemic Logic Erotetic Logic Higher-Order Logic Modal and Intensional Logic Nonclassical Logics Temporal Logic Logics, Misc Logical Consequence and Entailment Logical Expressions Logical Constants Logical Connectives Quantifiers Variables Paradoxes Epistemic Paradoxes Liar Paradox Russell's Paradox Sorites Paradox Probabilistic Puzzles Decision-Theoretic Puzzles Paradoxes, Misc Logical Semantics and Logical Truth History of Logic Ancient Greek and Roman Logic Aristotelian Logic Buddhist Logic Indian Logic Medieval Logic 20th Century Logic 19th Century Logic History of Logic, Misc 17th/18th Century Logic Logic and Phil of Logic, Miscellaneous Dialetheism Epistemology of Logic Informal Logic Logical Expressivism Logical Pluralism Logic and Information Logic in Phil Model Theory Proof Theory Set Theory Mathematical Logic Introductions to Logic Logic and Phil of Logic, General Works Logic and Phil of Logic, Misc

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41. FMP-Ensuring Logics, RA-Ensuring Logics and FA-Ensuring Logics in $$\text {NExtK4.3}$$.Ming Xu - 2023 - Studia Logica 111 (6):899-946.
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 $$\{{\textbf{S}}_{k}\}_{k\in \omega }$$ and $$\{{\textbf{S}} _{k}^{*}\}_{k\in \omega }$$ of logics are presented, in terms of which the necessary and sufficient conditions are formulated as follows: A logic in (...)
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42. On Heyting Algebras with Negative Tense Operators.Federico G. Almiñana, Gustavo Pelaitay & William Zuluaga - 2023 - Studia Logica 111 (6):1015-1036.
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.
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43. C. I. Lewis’s Intensional Semantics.Edwin Mares - 2023 - Notre Dame Journal of Formal Logic 64 (3):329-352.
This paper begins with a discussion of C. I. Lewis’s theory of meaning in his book, An Analysis of Knowledge and Valuation (1946) and his pragmatic theory of analyticity and necessity. I bring this theories together with some remarks that he makes in an appendix to the second edition of Symbolic Logic to construct an algebraic semantics for his logics S2 and S3. These logics and their semantics are compared and evaluated with regard to how well they implement Lewis’s theories (...)
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44. Definable Version of Wedderburn–Artin Theorem in O-Minimal Structures.Jaruwat Rodbanjong & Athipat Thamrongthanyalak - 2023 - Notre Dame Journal of Formal Logic 64 (3):353-362.
Here we work in an arbitrary o-minimal expansion of a divisible ordered abelian group. We say that a definable ring is definably semiprime if squares of nontrivial two-sided ideals definable in the expansion are nontrivial. We prove a definable version of Wedderburn–Artin theorem and give a characterization of definably semiprime rings.
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45. On Unsuperstable Theories in Gdst.Miguel Moreno - forthcoming - Journal of Symbolic Logic:1-24.
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46. A Brain Without The Brain: A Paradigm Shift from Neural to Aneural Brain.Joey Lawsin - forthcoming - In Inscription by Design.
In this article, Joey Lawsin argues that intelligence, behaviors, perceptions, awareness, consciousness, and other related mental interims can be processed without the need of the brain. His claims are built upon the concepts of Inscription by Design and Generated Interim Emergence. The former deals with Intuitive Systems, Embedded Inscriptions, and Generated Interims while the latter deals with the new seven evolutionary criteria of life namely: (i) Mechanical Aliveness, (ii) Sensoric Awareness, (iii) Logical Intuitiveness, (iv) Aneural Consciousness, (v) Information Inlearness, (vi) (...)
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47. Wahrheit und logisches Schließen. [REVIEW]W. Stelzner - 2023 - History and Philosophy of Logic 44 (4):510-513.
As the titles of the two volumes indicate, the publication is a textbook on formal logic, whose first volume is aimed primarily at beginners, but in the volume on modal logic also has in mind those...
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48. A. Benitez, La Silogística de Aristóteles. [REVIEW]M. Dahlquist - 2023 - History and Philosophy of Logic 44 (4):505-507.
In La Silogística de Aristóteles, Antonio Benítez (i) offers a critical analysis of two contemporary interpretations of Aristotle's syllogistic of assertoric propositions (Corcoran and Łukasiewicz)...
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49. Russell Contra Sense/Reference, the ‘Mont Blanc’ Correspondence.Clare Hay - 2022 - History and Philosophy of Logic 44 (4):476-490.
It is argued that Russell before 1905 saw no value in Frege's sense/reference distinction. This is clearest in the Mont Blanc correspondence. It is argued that Russell and Frege failed to engage because Frege lacked a grasp on the internal/external relations distinction. For Russell sense is either an external relation, objectionably separating out thought and reference, or an internal relation, so what is thought is altered such that we do not know what we are talking about. The novelty of the (...)
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50. How to Distinguish Simple Objectless Ideas.Jan Claas - 2022 - History and Philosophy of Logic 44 (4):422-441.
Bernard Bolzano offers a criterion of individuation for ideas, according to which ideas are distinct if and only if they represent different objects or are composed differently. It fails to individuate ideas that are both simple and fail to represent, in particular syncategorematic ideas and logical constants. However, Bolzano also provides the means to close this gap. He suggests that we can distinguish ideas if they are not substitutable for each other in propositions, which we can, in turn, distinguish in (...)
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 Logics Classical Logic Deontic Logic Epistemic Logic Erotetic Logic Higher-Order Logic Modal and Intensional Logic Nonclassical Logics Temporal Logic Logics, Misc Logical Consequence and Entailment Logical Expressions Logical Constants Logical Connectives Quantifiers Variables Paradoxes Epistemic Paradoxes Liar Paradox Russell's Paradox Sorites Paradox Probabilistic Puzzles Decision-Theoretic Puzzles Paradoxes, Misc Logical Semantics and Logical Truth History of Logic Ancient Greek and Roman Logic Aristotelian Logic Buddhist Logic Indian Logic Medieval Logic 20th Century Logic 19th Century Logic History of Logic, Misc 17th/18th Century Logic Logic and Phil of Logic, Miscellaneous Dialetheism Epistemology of Logic Informal Logic Logical Expressivism Logical Pluralism Logic and Information Logic in Phil Model Theory Proof Theory Set Theory Mathematical Logic Introductions to Logic Logic and Phil of Logic, General Works Logic and Phil of Logic, Misc