Related papers: Turning the Liar paradox into a metatheorem of Bas…
We conjecture that the relative unpopularity of logical frameworks among practitioners is partly due to their complex meta-languages, which often demand both programming skills and theoretical knowledge of the meta-language in question for…
In this paper we make a contribution to the unification of formal models of defeasible reasoning. We present several translations between formal argumentation frameworks and nonmonotonic logics for reasoning with plausible assumptions. More…
The Natural Language Inference (NLI) task is an important task in modern NLP, as it asks a broad question to which many other tasks may be reducible: Given a pair of sentences, does the first entail the second? Although the state-of-the-art…
Verbs form the backbone of language, providing the structure and meaning to sentences. Yet, their intricate semantic nuances pose a longstanding challenge. Understanding verb relations through the concept of lexical entailment is crucial…
Explaining autonomous and intelligent systems is critical in order to improve trust in their decisions. Counterfactuals have emerged as one of the most compelling forms of explanation. They address ``why not'' questions by revealing how…
Pater's target article builds a persuasive case for establishing stronger ties between theoretical linguistics and connectionism (deep learning). This commentary extends his arguments to semantics, focusing in particular on issues of…
We introduce a new variant of dependence logic called Boolean dependence logic. In Boolean dependence logic dependence atoms are of the type =(x_1,...,x_n,\alpha), where \alpha is a Boolean variable. Intuitively, with Boolean dependence…
We construct a formal theory, which we call reflectica, whose language possesses the following properties of natural language: it is a self-reflecting language and an intensional language. By a self-reflecting language we understand an…
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…
The fundamental proposal in this article is that logical formulas of the form (f <-> ~f) are not contradictions, and that formulas of the form (t <-> t) are not tautologies. Such formulas, wherever they appear in mathematics, are instead…
We present a logic named L_{LF} whose intended use is to formalize properties of specifications developed in the dependently typed lambda calculus LF. The logic is parameterized by the LF signature that constitutes the specification. Atomic…
In this paper we concentrate on the nature of the liar paradox as a cognitive entity; a consistently testable configuration of properties. We elaborate further on a quantum mechanical model [Aerts, Broekaert, Smets 1999] that has been…
Natural Language Inference (NLI), also known as Recognizing Textual Entailment (RTE), is one of the most important problems in natural language processing. It requires to infer the logical relationship between two given sentences. While…
We give a novel approach to proving soundness and completeness for a logic (henceforth: the object-logic) that bypasses truth-in-a-model to work directly with validity. Instead of working with specific worlds in specific models, we reason…
Reynolds' parametricity originally equips types with proof-irrelevant binary propositional relations over the types. But such relations can also be taken proof-relevant or unary, and described either in an indexed or fibred way.…
The notion of non-deterministic logical matrix (where connectives are interpreted as multi-functions) preserves many good properties of traditional semantics based on logical matrices (where connectives are interpreted as functions) whilst…
This paper considers quasi-reductivity - essentially, the property that an evaluation cannot get "stuck" due to a missing case in pattern matching - in the context of term rewriting with logical constraints.
We extend the {\lambda}-calculus with constructs suitable for relational and functional-logic programming: non-deterministic choice, fresh variable introduction, and unification of expressions. In order to be able to unify…
In this paper we examine various requirements on the formalisation choices under which self-reference can be adequately formalised in arithmetic. In particular, we study self-referential numberings, which immediately provide a strong notion…
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…