Related papers: An overview of Generalised Veltman Semantics
We extend description logics (DLs) with non-monotonic reasoning features. We start by investigating a notion of defeasible subsumption in the spirit of defeasible conditionals as studied by Kraus, Lehmann and Magidor in the propositional…
Call a semantics for a language with variables absolute when variables map to fixed entities in the denotation. That is, a semantics is absolute when the denotation of a variable a is a copy of itself in the denotation. We give a trio of…
We provide a generalisation of Kripke semantics for Petr Hajek's Basic Logic and prove soundness and completeness of the same with respect to our semantics. We find this semantics easily specialises to the linearly-ordered Kripke frames for…
Texts in natural language contain a lot of temporal information, both explicit and implicit. Verbs and temporal adjuncts carry most of the explicit information, but for a full understanding general world knowledge and default assumptions…
The interpretability logic of a mathematical theory describes the structural behavior of interpretations over that theory. Different theories have different logics. This paper from 2011 revolves around the question what logic describes the…
This is a short paper about the relationship between logic and computation. More specifically, it is about a relationship between the completeness proof for intuitionistic propositional logic within the form of proof-theoretic semantics…
Large Language Models (LLMs) such as ChatGPT demonstrated the potential to replicate human language abilities through technology, ranging from text generation to engaging in conversations. However, it remains controversial to what extent…
In 1952 P. F. Strawson proposed a logic of presuppositions. It is an interpretation of Aristotelian logic, i.e. of the logic of the traditional syllogism. In 1981 Richard Diaz published a monograph in which he presented truth-relevant…
In 1933, G\"odel considered two modal approaches to describing provability. One captured formal provability and resulted in the logic GL and Solovay's Completeness Theorem. The other was based on the modal logic S4 and led to Artemov's…
This article is motivated by the fact that there is a distinction between the descriptions of logical explosion from syntactic and semantic points of view. The discussion is illustrated using the concept of abstract model structures and the…
Justification theory is a general framework for the definition of semantics of rule-based languages that has a high explanatory potential. Nested justification systems, first introduced by Denecker et al. (2015), allow for the composition…
Although neural sequence-to-sequence models have been successfully applied to semantic parsing, they fail at compositional generalization, i.e., they are unable to systematically generalize to unseen compositions of seen components.…
Provability logic GLP is well-known to be incomplete w.r.t. Kripke semantics. A natural topological semantics of GLP interprets modalities as derivative operators of a polytopological space. Such spaces satisfying all the axioms of GLP are…
Distributional semantics is the linguistic theory that a word's meaning can be derived from its distribution in natural language (i.e., its use). Language models are commonly viewed as an implementation of distributional semantics, as they…
Ontologies formalise how the concepts from a given domain are interrelated. Despite their clear potential as a backbone for explainable AI, existing ontologies tend to be highly incomplete, which acts as a significant barrier to their more…
Why should computers interpret language incrementally? In recent years psycholinguistic evidence for incremental interpretation has become more and more compelling, suggesting that humans perform semantic interpretation before constituent…
Large Language Models (LLMs) are becoming increasingly popular in pervasive computing due to their versatility and strong performance. However, despite their ubiquitous use, the exact mechanisms underlying their outstanding performance…
We revisit the duality between Kripke and algebraic semantics of intuitionistic and intuitionistic modal logic. We find that there is a certain mismatch between the two semantics, which means that not all algebraic models can be embedded…
I deal with two approaches to proof-theoretic semantics: one based on argument structures and justifications, which I call reducibility semantics, and one based on consequence among (sets of) formulas over atomic bases, called base…
The primary goal of this paper is to recast the semantics of modal logic, and dynamic epistemic logic (DEL) in particular, in category-theoretic terms. We first review the category of relations and categories of Kripke frames, with…