Related papers: A Categorical Semantics for Linear Logical Framewo…
We propose a new cubical type theory, termed (self-deprecatingly) the naive cubical type theory, and study its semantics using the universe category framework, which is similar to Uemura's categories with representable morphisms. In…
We study probabilistic team semantics which is a semantical framework allowing the study of logical and probabilistic dependencies simultaneously. We examine and classify the expressive power of logical formalisms arising by different…
We explore a proof language for intuitionistic multiplicative additive linear logic, incorporating the sup connective that introduces additive pairs with a probabilistic elimination, and sum and scalar products within the proof-terms. We…
Process theories combine a graphical language for compositional reasoning with an underlying categorical semantics. They have been successfully applied to fields such as quantum computation, natural language processing, linear dynamical…
Most categorical models for dependent types have traditionally been heavily set based: contexts form a category, and for each we have a set of types in said context -- and for each type a set of terms of said type. This is the case for…
In this paper we define intensional models for the classical theory of types, thus arriving at an intensional type logic ITL. Intensional models generalize Henkin's general models and have a natural definition. As a class they do not…
In [Ben13], the notion of logically distributive category has been introduced to provide a sound and complete semantics to multi-sorted first-order logical theories based on intuitionistic logic. In this note, it will be shown that the…
This paper presents a simple decidable logic of functional dependence LFD, based on an extension of classical propositional logic with dependence atoms plus dependence quantifiers treated as modalities, within the setting of generalized…
Native type systems are those in which type constructors are derived from term constructors, as well as the constructors of predicate logic and intuitionistic type theory. We present a method to construct native type systems for a broad…
We present a unifying framework for type systems for process calculi. The core of the system provides an accurate correspondence between essentially functional processes and linear logic proofs; fragments of this system correspond to…
We present a process semantics for the purely additive fragment of linear logic in which formulas denote protocols and (equivalence classes of) proofs denote multi-channel concurrent processes. The polycategorical model induced by this…
We define a general class of dependent type theories, encompassing Martin-L\"of's intuitionistic type theories and variants and extensions. The primary aim is pragmatic: to unify and organise their study, allowing results and constructions…
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.…
Logics with team semantics provide alternative means for logical characterization of complexity classes. Both dependence and independence logic are known to capture non-deterministic polynomial time, and the frontiers of tractability in…
Canonical extension has proven to be a powerful tool in algebraic study of propositional logics. In this paper we describe a generalization of the theory of canonical extension to the setting of first order logic. We define a notion of…
The notion of linear exponential comonads on symmetric monoidal categories has been used for modelling the exponential modality of linear logic. In this paper we introduce linear exponential comonads on general (possibly non-symmetric)…
We propose a cognitively and linguistically motivated set of sorts for lexical semantics in a compositional setting: the classifiers in languages that do have such pronouns. These sorts are needed to include lexical considerations in a…
The present work presents some results about the categorial relation between logics and its categories of structures. A (propositional, finitary) logic is a pair given by a signature and Tarskian consequence relation on its formula algebra.…
This paper investigates modal type theories by using a new categorical semantics called change-of-base semantics. Change-of-base semantics is novel in that it is based on (possibly infinitely) iterated enrichment and interpretation of…
We develop a second-order extension of intuitionistic modal logic, allowing quantification over propositions, both syntactically and semantically. A key feature of second-order logic is its capacity to define positive connectives from the…