Related papers: Intuitionistic Common Knowledge
In this paper, we present an alternative interpretation of propositional inquisitive logic as an epistemic logic of knowing how. In our setting, an inquisitive logic formula $\alpha$ being supported by a state is formalized as "knowing how…
This paper investigates the contingency of logic within the framework of possible world semantics. Possible world semantics captures the meaning of necessitation, i.e., a statement is necessarily true if it holds in all possible worlds.…
We show that intuitionistic propositional logic is \emph{Carnap categorical}: the only interpretation of the connectives consistent with the intuitionistic consequence relation is the standard interpretation. This holds relative to the most…
This work is a mathematician's attempt to understand intuitionistic logic. It can be read in two ways: as a research paper interspersed with lengthy digressions into rethinking of standard material; or as an elementary (but highly…
We consider the problem of answering queries about formulas of first-order logic based on background knowledge partially represented explicitly as other formulas, and partially represented as examples independently drawn from a fixed…
In this paper we investigate the fragment of intuitionistic logic which only uses conjunction (meet) and implication, using finite duality for distributive lattices and universal models. We give a description of the finitely generated…
The usual reading of logical implication "A implies B" as "if A then B" fails in intuitionistic logic: there are formulas A and B such that "A implies B" is not provable, even though B is provable whenever A is provable. Intuitionistic…
Bi-intuitionistic logic is the conservative extension of intuitionistic logic with a connective dual to implication. It is sometimes presented as a symmetric constructive subsystem of classical logic. In this paper, we compare three sequent…
Heyting-Lewis Logic is the extension of intuitionistic propositional logic with a strict implication connective that satisfies the constructive counterparts of axioms for strict implication provable in classical modal logics. Variants of…
This paper introduces two sequent calculi for intuitionistic strong L\"ob logic ${\sf iSL}_\Box$: a terminating sequent calculus ${\sf G4iSL}_\Box$ based on the terminating sequent calculus ${\sf G4ip}$ for intuitionistic propositional…
Circular (or cyclic) proofs have received increasing attention in recent years, and have been proposed as an alternative setting for studying (co)inductive reasoning. In particular, now several type systems based on circular reasoning have…
Epistemic logics typically talk about knowledge of individual agents or groups of explicitly listed agents. Often, however, one wishes to express knowledge of groups of agents specified by a given property, as in `it is common knowledge…
This paper establishes the normalisation of natural deduction or lambda calculus formulation of Intuitionistic Non Commutative Logic --- which involves both commutative and non commutative connectives. This calculus first introduced by de…
Three classes of models of QHC, the joint logic of problems and propositions, are constructed, including a class of subset/sheaf-valued models that is related to solutions of some actual problems (such as solutions of algebraic equations).…
Continual learning enables incremental learning of new tasks without forgetting those previously learned, resulting in positive knowledge transfer that can enhance performance on both new and old tasks. However, continual learning poses new…
In this paper, we delve into the study of epistemic logics, interpreted through similarity models based on weighted graphs. We explore eight languages that extend the traditional epistemic language by incorporating modalities of common,…
We present the logic iJT4, which is an explicit version of intuitionistic S4 and establish soundness and completeness with respect to modular models.
Several different proof translations exist between classical and intuitionistic logic (negative translations), and intuitionistic and linear logic (Girard translations). Our aims in this paper are (1) to consider extensions of…
We prove that the propositional logic of intuitionistic set theory IZF is intuitionistic propositional logic IPC. More generally, we show that IZF has the de Jongh property with respect to every intermediate logic that is complete with…
We introduce an intuitionistic modal logic strictly contained in the intuitionistic modal logic IK and being an appropriate candidate for the title of ``minimal normal intuitionistic modal logic''.