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This reports introduces a novel sound and complete semantics for first order intuitionistic logic, in the framework of category theory and by the computational interpretation of the logic based on the so-called Curry-Howard isomorphism.…
Provability logics are modal or polymodal systems designed for modeling the behavior of G\"odel's provability predicate in arithmetical theories and its natural extensions. If \Lambda is any ordinal, the G\"odel-L\"ob calculus GLP(\Lambda)…
We combine the concepts of modal logics and many-valued logics in a general and comprehensive way. Namely, given any finite linearly ordered set of truth values and any set of propositional connectives defined by truth tables, we define the…
A system of linear dependent types for the lambda calculus with full higher-order recursion, called dlPCF, is introduced and proved sound and relatively complete. Completeness holds in a strong sense: dlPCF is not only able to precisely…
The study of modal logic has witnessed tremendous development following the introduction of Kripke semantics. However, recent developments in programming languages and type theory have led to a second way of studying modalities, namely…
A type theory is presented that combines (intuitionistic) linear types with type dependency, thus properly generalising both intuitionistic dependent type theory and full linear logic. A syntax and complete categorical semantics are…
Inquisitive modal logic, InqML, is a generalisation of standard Kripke-style modal logic. In its epistemic incarnation, it extends standard epistemic logic to capture not just the information that agents have, but also the questions that…
Intuitionistic logic extended with decidable propositional atoms combines classical properties in its propositional part and intuitionistic properties for derivable formulas not containing propositional symbols. Sequent calculus is used as…
Monads in category theory are algebraic structures that can be used to model computational effects in programming languages. We show how the notion of "centre", and more generally "centrality", i.e. the property for an effect to commute…
We present a polymorphic linear lambda-calculus as a proof language for second-order intuitionistic linear logic. The calculus includes addition and scalar multiplication, enabling the proof of a linearity result at the syntactic level.
Propositional term modal logic is interpreted over Kripke structures with unboundedly many accessibility relations and hence the syntax admits variables indexing modalities and quantification over them. This logic is undecidable, and we…
A type theory is presented that combines (intuitionistic) linear types with type dependency, thus properly generalising both intuitionistic dependent type theory and full linear logic. A syntax and complete categorical semantics are…
Generalizing standard monadic second-order logic for Kripke models, we introduce monadic second-order logic interpreted over coalgebras for an arbitrary set functor. We then consider invariance under behavioral equivalence of MSO-formulas.…
Recent advances in programming languages study and design have established a standard way of grounding computational systems representation in category theory. These formal results led to a better understanding of issues of control and…
We study a conservative extension of classical propositional logic distinguishing between four modes of statement: a proposition may be affirmed or denied, and it may be strong or classical. Proofs of strong propositions must be…
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…
The paper is dedicated to the problem of adding a modality to the \Lukasiewicz many-valued logics in the purpose of obtaining completeness results for Kripke semantics. We define a class of modal many-valued logics and their corresponding…
In this paper, we study a new Kripke-style semantics for classical modal logic, named as provability models. We study provability models for the propositional modal logics K, K4, S4 GL, GLP and the interpretability logic ILM. Provability…
In [17], we introduced a modal logic, called $L$, which combines intuitionistic propositional logic $IPC$ and classical propositional logic $CPC$ and is complete w.r.t. an algebraic semantics. However, $L$ seems to be too weak for…
The lambda calculus with constructors is an extension of the lambda calculus with variadic constructors. It decomposes the pattern-matching a la ML into a case analysis on constants and a commutation rule between case and application…