相关论文: Three Dogmas, a Puzzle and its Solution

The four-valued semantics of Belnap--Dunn logic, consisting of the truth values True, False, Neither, and Both, gives rise to several non-classical logics depending on which feature of propositions we wish to preserve: truth, non-falsity,…

For formulas F of propositional calculus I introduce a "metavariable" MF and show how it can be used to define an algorithm for testing satisfiability. MF is a formula which is true/false under all possible truth assignments iff F is…

We present a proof-theoretic analysis of the logic NL$\lambda$ (Barker \& Shan 2014, Barker 2019). We notably introduce a novel calculus of proof nets and prove it is sound and complete with respect to the sequent calculus for the logic. We…

In this paper we propose an approach to reasoning about properties of imperative programs. We assume in this context that the meanings of program constructs are described using rules in the natural semantics style with the additional…

We develop a system for solving logical deduction one-dimensional ordering problems by transforming natural language premises and candidate statements into first-order logic. Building on Heim and Kratzer's syntax-based compositional…

Recent progress in natural language processing (NLP) owes much to remarkable advances in large language models (LLMs). Nevertheless, LLMs frequently "hallucinate," resulting in non-factual outputs. Our carefully-designed human evaluation…

Recently, symbolic structures were proposed as finite representations of potentially infinite first-order structures, where Linear Integer Arithmetic terms and formulas define the domain and interpretations of a structure. We generalize…

The Semantic Web drives towards the use of the Web for interacting with logically interconnected data. Through knowledge models such as Resource Description Framework (RDF), the Semantic Web provides a unifying representation of richly…

Unlike autoregressive models, which generate tokens sequentially and benefit from reasoning-before-answering strategies such as Chain-of-Thought, Masked Diffusion Language Models (MDLMs) refine all sequence positions simultaneously, raising…

We revisit the issue of connections between two leading formalisms in nonmonotonic reasoning: autoepistemic logic and default logic. For each logic we develop a comprehensive semantic framework based on the notion of a belief pair. The set…

Modern physics is founded on two mainstays: mathematical modelling and empirical verification. These two assumptions are prerequisite for the objectivity of scientific discourse. Here we show, however, that they are contradictory, leading…

Evaluating natural language generation (NLG) systems remains a core challenge of natural language processing (NLP), further complicated by the rise of large language models (LLMs) that aims to be general-purpose. Recently, large language…

Reasoning with quantifier expressions in natural language combines logical and arithmetical features, transcending strict divides between qualitative and quantitative. Our topic is this cooperation of styles as it occurs in common…

Large Language Models (LLMs) are deployed as powerful tools for several natural language processing (NLP) applications. Recent works show that modern LLMs can generate self-explanations (SEs), which elicit their intermediate reasoning steps…

Bilateralists hold that the meanings of the connectives are determined by rules of inference for their use in deductive reasoning with asserted and denied formulas. This paper presents two bilateral connectives comparable to Prior's tonk,…

In this article, we present a fresh perspective on language, combining ideas from various sources, but mixed in a new synthesis. As in the minimalist program, the question is whether we can formulate an elegant formalism, a universal…

While in recent years machine learning (ML) based approaches have been the popular approach in developing end-to-end question answering systems, such systems often struggle when additional knowledge is needed to correctly answer the…

Tarski's undefinability theorem states that a formal system based on conventional predicate logic (PL) cannot talk about its own truth predicate. PL is, however, not the only formal language imaginable. In this paper, it will be shown that…

Many-valued models generalise the structures from classical model theory by defining truth values for a model with an arbitrary algebra. Just as algebraic varieties provide semantics for many non-classical propositional logics, models…

Human beings possess the most sophisticated computational machinery in the known universe. We can understand language of rich descriptive power, and communicate in the same environment with astonishing clarity. Two of the many contributors…