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We develop a correspondence between the theory of sequential algorithms and classical reasoning, via Kreisel's no-counterexample interpretation. Our framework views realizers of the no-counterexample interpretation as dynamic processes…
This article initiates the semantic study of distribution-free normal modal logic systems, laying the semantic foundations and anticipating further research in the area. The article explores roughly the same area, though taking a different…
Based on an analysis of the inference rules used, we provide a characterization of the situations in which classical provability entails intuitionistic provability. We then examine the relationship of these derivability notions to uniform…
In an article dating back in 1992, Kosta Do\v{s}en initiated a project of modal translations in substructural logics, aiming at generalizing the well-known G\"{o}del-McKinsey-Tarski translation of intuitionistic logic into {\bf S4}.…
Linear implication can represent state transitions, but real transition systems operate under temporal, stochastic or probabilistic constraints that are not directly representable in ordinary linear logic. We propose a general modal…
We introduce refutationally complete superposition calculi for intentional and extensional clausal $\lambda$-free higher-order logic, two formalisms that allow partial application and applied variables. The calculi are parameterized by a…
We propose an extension of Poole's independent choice logic based on a relaxation of the underlying independence assumptions. A credal semantics involving multiple joint probability mass functions over the possible worlds is adopted. This…
In this paper we explore the design of sequent calculi operating on graphs. For this purpose, we introduce a set of logical connectives allowing us to extend the correspondence between cographs and classical propositional formulas to any…
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…
For a commutative algebra which comes from a Zinbiel algebra the exponential series can be written without denominators. When lifted to dendriform algebras this new series satisfies a functional equation analogous to the…
Sahlqvist theory is extended to the fragments of the intuitionistic propositional calculus that include the conjunction connective. This allows us to introduce a Sahlqvist theory of intuitionistic character amenable to arbitrary…
Defeasible logic is a rule-based nonmonotonic logic, with both strict and defeasible rules, and a priority relation on rules. We show that inference in the propositional form of the logic can be performed in linear time. This contrasts…
We add to intuitionistic logic infinitely many classical disjunctive tautologies and use the Curry--Howard correspondence to obtain typed concurrent $\lambda$-calculi; each of them features a specific communication mechanism, including…
Recent published work has addressed the Shalqvist correspondence problem for non-distributive logics. The natural question that arises is to identify the fragment of first-order logic that corresponds to logics without distribution, lifting…
Intersection types are an essential tool in the analysis of operational and denotational properties of lambda-terms and functional programs. Among them, non-idempotent intersection types provide precise quantitative information about the…
This paper shows how to derive nested calculi from labelled calculi for propositional intuitionistic logic and first-order intuitionistic logic with constant domains, thus connecting the general results for labelled calculi with the more…
We provide the first (non-labelled) sequent calculi for bimodal provability logics with "usual" provability predicates. In particular, we introduce calculi for the logics CS, CSM and ER. Additionally, we present non-wellfounded versions of…
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…
In this paper we investigate certain systems of propositional intuitionistic modal logic defined semantically in terms of neighborhood structures. We discuss various restrictions imposed on those frames but our constant approach is to…
We present a comprehensive programme analysing the decomposition of proof systems for non-classical logics into proof systems for other logics, especially classical logic, using an algebra of constraints. That is, one recovers a proof…