Gheorghiu, Alexander V;
(2024)
Investigations into Semantics in Reductive Logic.
Doctoral thesis (Ph.D), UCL (University College London).
Preview |
Text
Thesis___Alex (1).pdf - Accepted Version Download (1MB) | Preview |
Abstract
Logic is the study of reasoning. Typically, it proceeds in terms of inferring a conclusion from established premises. The systematic use of symbolic and mathematical techniques to determine the forms of valid reasoning on this plan determines Deductive Logic. Reductive Logic is the dual paradigm that proceeds by generating from a putative conclusion a set of sufficient premises. While logical consequence can be characterized through proof-theoretic and semantic approaches, work in Reductive Logic has traditionally focused on the former. This monograph is composed of three parts that illustrate the interplay between semantics and proof in Reductive Logic: Part I comprises a case-study, Part II develops tools and gives result for a more general account, and Part III considers a semantics entirely based on notions of proofs. These a briefly outlined below. In Part I, the monograph examines proof-search in the logic of Bunched Implications (BI), presenting technical results such as cut-elimination, logic programming, and focusing. It also illustrates a novel approach to soundness and complete- ness (S&C) for BI that proceeds entirely through proof-search methods, eliminating the need for constructing term- and counter-models. In Part II, the monograph introduces and develops the theory of a paradigm of proof system called ‘algebraic constraint systems’ (ACSs). Briefly, ACSs are sequent calculi enriched with an algebra over which constraints are generated during reduction that, when solved, determine a proof. They help bridge the gap between proof theory and semantics in Reductive Logic. In particular, the part uses ACSs for the following: to provide a general account of the approach to S&C studied in BI; to systematically generate relational calculi for logics that satisfy specific conditions; and to derive a semantics of IPL from its proof theory. In Part III, the monograph explores proof-theoretic semantics — the approach to meaning in logic based on proof rather than truth — and provides both general insights and a range of technical results. While the monograph contains several contributions to logic across mathematics, informatics, and philosophy, its real contribution is to demonstrate the viability and merit of studying semantics from the perspective of Reductive Logic and to give methods, techniques, and tools for a systematic theory to be developed.
| Type: | Thesis (Doctoral) |
|---|---|
| Qualification: | Ph.D |
| Title: | Investigations into Semantics in Reductive Logic |
| Open access status: | An open access version is available from UCL Discovery |
| Language: | English |
| Additional information: | Copyright © The Author 2024. Original content in this thesis is licensed under the terms of the Creative Commons Attribution-NonCommercial 4.0 International (CC BY-NC 4.0) Licence (https://creativecommons.org/licenses/by-nc/4.0/). Any third-party copyright material present remains the property of its respective owner(s) and is licensed under its existing terms. Access may initially be restricted at the author’s request. |
| UCL classification: | UCL UCL > Provost and Vice Provost Offices > UCL BEAMS UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Engineering Science UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Engineering Science > Dept of Computer Science |
| URI: | https://discovery.ucl.ac.uk/id/eprint/10188010 |
Loading...
Loading...Loading...Loading...Archive Staff Only
 |
View Item |
