Related papers: Non-distributive logics: from semantics to meaning
We provide an overview of the hybrid compositional distributional model of meaning, developed in Coecke et al. (arXiv:1003.4394v1 [cs.CL]), which is based on the categorical methods also applied to the analysis of information flow in…
We present a general relational semantics framework which, by varying the axiomatization and components of the relational structures, provides a uniform semantics for sentential logics, classical and non-classical alike. The approach we…
We introduce and investigate a family of consequence relations with the goal of capturing certain important patterns of data-driven inference. The inspiring idea for our framework is the fact that data may reject, possibly to some degree,…
Separation logic is a recent extension of Hoare logic for reasoning about programs with references to shared mutable data structures. In this paper, we provide a new interpretation of the logic for a programming language with higher types.…
We investigate some basic questions about the interaction of regular and rational relations on words. The primary motivation comes from the study of logics for querying graph topology, which have recently found numerous applications. Such…
This paper surveys main and recent studies on temporal logics in a broad sense by presenting various logic systems, dealing with various time structures, and discussing important features, such as decidability (or undecidability) results,…
Logical relations built on top of an operational semantics are one of the most successful proof methods in programming language semantics. In recent years, more and more expressive notions of operationally-based logical relations have been…
This article presents an overview of computability logic -- the game-semantically constructed logic of interactive computational tasks and resources. There is only one non-overview, technical section in it, devoted to a proof of the…
The Expansion property considered by researchers in Social Choice is shown to correspond to a logical property of nonmonotonic consequence relations that is the {\em pure}, i.e., not involving connectives, version of a previously known weak…
In this work we describe preferential Description Logics of typicality, a nonmonotonic extension of standard Description Logics by means of a typicality operator T allowing to extend a knowledge base with inclusions of the form T(C) v D,…
Understanding the semantic relationships between terms is a fundamental task in natural language processing applications. While structured resources that can express those relationships in a formal way, such as ontologies, are still scarce,…
We construct a denotational model of linear logic, whose objects are all the locally convex and separated topological vector spaces endowed with their weak topology. The negation is interpreted as the dual, linear proofs are interpreted as…
Logical reasoning is central to human cognition and intelligence. It includes deductive, inductive, and abductive reasoning. Past research of logical reasoning within AI uses formal language as knowledge representation and symbolic…
This article aims to provide a unified and technical approach to semantic information, communication, and their interplay through the lens of probabilistic logic. To this end, on top of the existing technical communication (TC) layer, we…
Semantically non-compositional phrases constitute an intriguing research topic in Natural Language Processing. Semantic non-compositionality --the situation when the meaning of a phrase cannot be derived from the meaning of its components,…
Ontologies enable knowledge sharing and interdisciplinary collaboration by providing standardized, structured vocabularies for diverse communities. While logical axioms are a cornerstone of ontology design, natural language elements such as…
This paper introduces context algebras and demonstrates their application to combining logical and vector-based representations of meaning. Other approaches to this problem attempt to reproduce aspects of logical semantics within new…
Justification logics are modal-like logics with the additional capability of recording the reason, or justification, for modalities in syntactic structures, called justification terms. Justification logics can be seen as explicit…
We develop a common semantic framework for the interpretation both of $\mathbf{IPC}$, the intuitionistic propositional calculus, and of logics weaker than $\mathbf{IPC}$ (substructural and subintuitionistic logics). This is done by proving…
Data-driven representation learning for words is a technique of central importance in NLP. While indisputably useful as a source of features in downstream tasks, such vectors tend to consist of uninterpretable components whose relationship…