Related papers: Lectures on Jacques Herbrand as a Logician
The aim of our paper is twofold: firstly we present a sequent calculus for an intuitionistic non-Fregean logic ISCI, which is based on the calculus presented in the paper by Chlebowski and Leszczynska-Jasion, 'An Investigation into…
We examine the classical/intuitionist divide, and how it reflects on modern theories of infinitesimals. When leading intuitionist Heyting announced that "the creation of non-standard analysis is a standard model of important mathematical…
We describe the layer of quantifier alternation depth at most one of the quantifier completion of a Boolean doctrine over a small category. This amounts to a doctrinal version of Herbrand's theorem for formulas with quantifier alternation…
Logic $L$ was introduced by Lewitzka [7] as a modal system that combines intuitionistic and classical logic: $L$ is a conservative extension of CPC and it contains a copy of IPC via the embedding $\varphi\mapsto\square\varphi$. In this…
I present the proof of Goedel's First Incompleteness theorem in an intuitive manner, while covering all technically challenging steps. I present generalizations of Goedel's fixed point lemma to two-sentence and multi-sentence versions,…
The fixed-point logic LREC= was developed by Grohe et al. (CSL 2011) in the quest for a logic to capture all problems decidable in logarithmic space. It extends FO+C, first-order logic with counting, by an operator that formalises a limited…
This work presents an operational and geometric approach to logic. It starts from the multilinear elective decomposition of binary logical functions in the original form introduced by George Boole. A justification on historical grounds is…
This book can be seen either as a text on theorem proving that uses techniques from general algebra, or else as a text on general algebra illustrated and made concrete by practical exercises in theorem proving. The book considers several…
Hilbert's Entscheidungsproblem has given rise to a broad and productive line of research in mathematical logic, where the classification process of decidable classes of first-order sentences represent only one of the remarkable results.…
We study abstract intermediate justification logics, that is arbitrary intermediate propositional logics extended with a subset of specific axioms of (classical) justification logics. For these, we introduce various semantics by combining…
Free variables occur frequently in mathematics and computer science with ad hoc and altering semantics. We present the most recent version of our free-variable framework for two-valued logics with properly improved functionality, but only…
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…
We study topology, particularly compactness, as an extension of Shulman's work on constructive mathematics via affine logic, while allowing propositional impredicativity. We introduce a notion of compactness in affine logic and prove the…
Indexed Linear Logic has been introduced by Ehrhard and Bucciarelli, it can be seen as a logical presentation of non-idempotent intersection types extended through the relational semantics to the full linear logic. We introduce an…
Fundamental logic was introduced by Wesley Holliday (2023) to unify intuitionistic logic and quantum logic from a proof-theoretic perspective, capturing the logic determined solely by the introduction and elimination rules of connectives…
The formalism of abstracted quantum mechanics is applied in a model of the generalized Liar Paradox. Here, the Liar Paradox, a consistently testable configuration of logical truth properties, is considered a dynamic conceptual entity in the…
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…
When an agent can articulate why something works, we typically take this as evidence of genuine understanding. This presupposes that effective action and correct explanation covary, and that coherent explanation reliably signals both. I…
This work explores the connection between logical independence and the algebraic structure of quantum mechanics. Building on results by Brukner et al., it introduces the notion of \textit{onto-epistemic ignorance}: situations in which the…
Coherent differentiation was introduced by Ehrhard in order to generalize differential categories to a setting in which the sum is only partially defined, in order to account for the deterministic nature of most models of computation. This…