Related papers: Logical Inferentialism & Attacks on Classical Logi…

In this paper, we provide more evidence for the contention that logical consequence should be understood in normative terms. Hartry Field and John MacFarlane covered the classical case. We extend their work, examining what it means for an…

I formalize important theorems about classical propositional logic in the proof assistant Coq. The main theorems I prove are (1) the soundness and completeness of natural deduction calculus, (2) the equivalence between natural deduction…

Inferring from inconsistency and making decisions are two problems which have always been treated separately by researchers in Artificial Intelligence. Consequently, different models have been proposed for each category. Different…

This article was motivated by the discovery of a potential new foundation for mainstream mathematics. The goals are to clarify the relationships between primitives, foundations, and deductive practice; to understand how to determine what…

Can a physicist make only a finite number of errors in the eternal quest to uncover the law of nature? This millennium-old philosophical problem, known as inductive inference, lies at the heart of epistemology. Despite its significance to…

This paper discusses proof-theoretic semantics, the project of specifying the meanings of the logical constants in terms of rules of inference governing them. I concentrate on Michael Dummett's and Dag Prawitz' philosophical motivations and…

Intuitively, the more powerful a theory is, the greater the variety and quantity of ideas can be expressed through its formal language. Therefore, when comparing two theories concerning the same subject, it seems only reasonable to compare…

Dummett's logic LC is intuitionistic logic extended with Dummett's axiom: for every two statements the first implies the second or the second implies the first. We present a natural deduction and a Curry-Howard correspondence for…

Large language models exhibit systematic limitations in structured logical reasoning: they conflate hypothesis generation with verification, cannot distinguish conjecture from validated knowledge, and allow weak reasoning steps to propagate…

In this paper we will see deductive systems for classical propositional and predicate logic in the calculus of structures. Like sequent systems, they have a cut rule which is admissible. In addition, they enjoy a top-down symmetry and some…

At the onset of quantum mechanics, it was argued that the new theory would entail a rejection of classical logic. The main arguments to support this claim come from the non-commutativity of quantum observables, which allegedly would…

An indeterministic interpretation of classical physics has been proposed recently, in which the argument relies on attacking an alleged unwarranted metaphysical hidden assumption of the standard deterministic interpretation. This short…

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,…

This paper explores proof-theoretic aspects of hybrid type-logical grammars , a logic combining Lambek grammars with lambda grammars. We prove some basic properties of the calculus, such as normalisation and the subformula property and also…

We present a framework for deriving inference relations between Dutch sentence pairs. The proposed framework relies on logic-based reasoning to produce inspectable proofs leading up to inference labels; its judgements are therefore…

As it is well known, classical mechanics consists of several basic features like determinism, reductionism, completeness of knowledge and mechanicism. In this article the basic assumptions are discussed which underlie those features. It is…

Comparative constructions pose a challenge in Natural Language Inference (NLI), which is the task of determining whether a text entails a hypothesis. Comparatives are structurally complex in that they interact with other linguistic…

We propose a semantic representation of the standard quantum logic QL within a classical, normal modal logic, and this via a lattice-embedding of orthomodular lattices into Boolean algebras with one modal operator. Thus our classical logic…

Because contemporary large software systems are pervasively inconsistent, it is not safe to reason about them using classical logic. The goal of Direct Logic is to be a minimal fix to classical mathematical logic that meets the requirements…

General relativity required the abandonment of Euclidean geometry. Here we show that quantum theory requires the abandonment of classical logic. We show that the Hilbert space representation of quantum theory is logically inevitable. There…