Related papers: Maximality of bi-intuitionistic propositional logi…

Bilateralists hold that the meanings of the connectives are determined by rules of inference for their use in deductive reasoning with asserted and denied formulas. This paper presents two bilateral connectives comparable to Prior's tonk,…

We explore various semantic understandings of dual intuitionistic logic by exploring the relationship between co-Heyting algebras and topological spaces. First, we discuss the relevant ideas in the setting of Heyting algebras and…

We bring forward a logical system of transition algebras that enhances many-sorted first-order logic using features from dynamic logics. The sentences we consider include compositions, unions, and transitive closures of transition…

With help of a compact Prolog-based theorem prover for Intuitionistic Propositional Logic, we synthesize minimal assumptions under which a given formula formula becomes a theorem. After applying our synthesis algorithm to cover basic…

In this note, by integrating ideas concerning terminating tableaux-based procedures in modal logics and finite frame property of intuitionistic modal logic IK, we provide new and simpler decidability proofs for FIK and LIK.

We present an illative system I_s of classical higher-order logic with subtyping and basic inductive types. The system I_s allows for direct definitions of partial and general recursive functions, and provides means for handling functions…

We consider (finitary, propositional) logics through the original use of Category Theory: the study of the "sociology of mathematical objects", aligning us with a recent, and growing, trend of study logics through its relations with other…

Expectation is a central notion in probability theory. The notion of expectation also makes sense for other notions of uncertainty. We introduce a propositional logic for reasoning about expectation, where the semantics depends on the…

In this paper we consider Modal Team Logic, a generalization of Classical Modal Logic in which it is possible to describe dependence phenomena between data. We prove that most known fragment of Full Modal Team Logic allow the elimination of…

A semantics is given to possibilistic logic, a logic that handles weighted classical logic formulae, and where weights are interpreted as lower bounds on degrees of certainty or possibility, in the sense of Zadeh's possibility theory. The…

Any intermediate propositional logic (i.e., a logic including intuitionistic logic and contained in classical logic) can be extended to a calculus with epsilon- and tau-operators and critical formulas. For classical logic, this results in…

Logic $L$ was introduced by Lewitzka [7] as a modal system that combines intuitionistic and classical logic: $L$ is a conservative extension of CPC and it contains a copy of IPC via the embedding $\varphi\mapsto\square\varphi$. In this…

We consider intuitionistic variants of linear temporal logic with `next', `until' and `release' based on expanding posets: partial orders equipped with an order-preserving transition function. This class of structures gives rise to a logic…

The formal construction of the second-order logic or predicate calculus essentially adds quantifiers to propositional logic. Why second-order logic cannot be reduced to that of the first order? How to demonstrate that certain predicates are…

In 1938, Tarski proved that a formula is not intuitionistically valid if, and only if, it has a counter-model in the Heyting algebra of open sets of some topological space. In fact, Tarski showed that any Euclidean space R^n with n >= 1…

We show that the intuitionistic propositional logic with a Galois connection (IntGC), introduced by the authors, has the finite model property.

We introduce a realisability semantics for infinitary intuitionistic set theory that is based on Ordinal Turing Machines (OTMs). We show that our notion of OTM-realisability is sound with respect to certain systems of infinitary…

MV-algebras are an algebraic semantics for Lukasiewicz logic and MV-algebras generated by a finite chain are Heyting algebras where the Godel implication can be written in terms of De Morgan and Moisil's modal operators. In our work, a…

In a previous work we introduced a non-associative non-commutative logic extended by multimodalities, called subexponentials, licensing local application of structural rules. Here, we further explore this system, considering a classical…

Otto's Theorem characterises the bisimulation-invariant PTIME queries over graphs as exactly those that can be formulated in the polyadic mu-calculus, hinging on the Immerman-Vardi Theorem which characterises PTIME (over ordered structures)…