Related papers: Classical linear logic, cobordisms and categorial …

We consider a proper propositional quantum logic and show that it has multiple disjoint lattice models, only one of which is an orthomodular lattice (algebra) underlying Hilbert (quantum) space. We give an equivalent proof for the classical…

Quantum logic aims to capture essential quantum mechanical structure in order-theoretic terms. The Achilles' heel of quantum logic is the absence of a canonical description of composite systems, given descriptions of their components. We…

This paper develops a systematic framework for integrating local categories that model logical connectives using higher category theory. By extending these local categories into a unified two-category enriched with natural isomorphisms, the…

A co-valuation is, essentially, a minimal finite cover. We introduce a logic based on co-valuations, which play the role of valuations of free variables in classical first-order logic, and show that the fundamental tools of model theory --…

Comparative constructions play an important role in natural language inference. However, attempts to study semantic representations and logical inferences for comparatives from the computational perspective are not well developed, due 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…

Modern categorical logic as well as the Kripke and topological models of intuitionistic logic suggest that the interpretation of ordinary "propositional" logic should in general be the logic of subsets of a given universe set. Partitions on…

We construct a symmetric monoidal closed category of polynomial endofunctors (as objects) and simulation cells (as morphisms). This structure is defined using universal properties without reference to representing polynomial diagrams and is…

We propose a new version of generalized probabilistic propositional logic, namely, discrete-continuous logic (DCL) in which every generalized proposition (GP) is represented as 2x2 nondiagonal positive matrix with unit trace. We demonstrate…

In this paper, we use a categorical and functorial set up to model the syntax and inference of logics with algebraic signature, extending previous works on algebraisation of logics. The main feature of this work is that structurality, or…

Abstract grammatical knowledge - of parts of speech and grammatical patterns - is key to the capacity for linguistic generalization in humans. But how abstract is grammatical knowledge in large language models? In the human literature,…

We present a method for coarse-grained cross-lingual alignment of comparable texts: segments consisting of contiguous paragraphs that discuss the same theme (e.g. history, economy) are aligned based on induced multilingual topics. The…

Differential categories were introduced to provide a minimal categorical doctrine for differential linear logic. Here we revisit the formalism and, in particular, examine the two different approaches to defining differentiation which were…

We give a new characterization of elementary and deterministic polynomial time computation in linear logic through the proofs-as-programs correspondence. Girard's seminal results, concerning elementary and light linear logic, achieve this…

Lambeks Syntactic Calculus, commonly referred to as the Lambek calculus, was innovative in many ways, notably as a precursor of linear logic. But it also showed that we could treat our grammatical framework as a logic (as opposed to a…

Substructural logics are formal logical systems that omit familiar structural rules of classical and intuitionistic logic such as contraction, weakening, exchange (commutativity), and associativity. This leads to a resource-sensitive…

We consider the non-deterministic extension of the call-by-value lambda calculus, which corresponds to the additive fragment of the linear-algebraic lambda-calculus. We define a fine-grained type system, capturing the right linearity…

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…

Coinductive definitions, such as that of an infinite stream, may often be described by elegant logic programs, but ones for which SLD-refutation is of no value as SLD-derivations fall into infinite loops. Such definitions give rise to…

This paper presents an abstract, mathematical formulation of classical propositional logic. It proceeds layer by layer: (1) abstract, syntax-free propositions; (2) abstract, syntax-free contraction-weakening proofs; (3) distribution; (4)…