Classification of (in)finitary logics
| Thesis title in Czech: | Klasifikace (in)finitárních logik |
|---|---|
| Thesis title in English: | Classification of (in)finitary logics |
| Key words: | Abstraktní algebraická logika, úplnost, relativně (konečně) subdirektně ireducibilní modely, RSI-úplnost, RFSI-úplnost, vlastnost rozšíření na (úplně) průsekové prvoteorie, IPEP, CIPEP. |
| English key words: | Abstract algebraic logic, completeness, relatively (finitely) subdirectly irreducible models, RSI-completeness, RFSI-completeness, (completely) intersection-prime extension property, IPEP, CIPEP. |
| Academic year of topic announcement: | 2013/2014 |
| Thesis type: | diploma thesis |
| Thesis language: | angličtina |
| Department: | Department of Logic (21-KLOG) |
| Supervisor: | Carles Noguera, Ph.D. |
| Author: | hidden - assigned and confirmed by the Study Dept. |
| Date of registration: | 23.06.2014 |
| Date of assignment: | 24.06.2014 |
| Administrator's approval: | not processed yet |
| Confirmed by Study dept. on: | 01.07.2014 |
| Date and time of defence: | 08.09.2015 09:00 |
| Date of electronic submission: | 10.08.2015 |
| Date of proceeded defence: | 08.09.2015 |
| Submitted/finalized: | committed by student and finalized |
| Opponents: | doc. Mgr. Michal Botur, Ph.D. |
| Guidelines |
| Abstract algebraic logic is the subdiscipline of mathematical logic that provides algebraic semantics for all propositional non-classical logics, produces hierarchies of classes of logics depending on the strength of their link with the algebraic semantics, and proves equivalences of various logical and algebraic notions. It is an active research area with many applications to the study of particular families of non-classical logics. In this master thesis we will concentrate on two lines of research: (1) study of general completeness theorems for wide classes of (non necessarily finitary) logics. We will consider the relations between extension properties, abstract forms of Lindenbaum lemma, existence bases of (finitely) intersection-irreducible theories and completeness with respect to (finitely) subdirectly irreducible models. (2) hierarchies of algebraizable and order-algebraizable logics, extending ideas from Blok, Pigozzi and Raftery on interpretation of logics in terms of equational and inequational consequence. In both lines, we will survey the known results and consider possible extensions. |
| References |
| W.J. Blok and D.L. Pigozzi. Algebraizable Logics, volume 396 of Memoirs of the American Mathematical Society. American Mathematical Society, Providence, RI, 1989. P. Cintula and C. Noguera. Implicational (semilinear) logics I: A new hierarchy. Archive for Mathematical Logic, 49(4):417-446, 2010. P. Cintula and C. Noguera. The proof by cases property and its variants in structural consequence relations. Studia Logica 101:713-747, 2013. J. Czelakowski. Protoalgebraic Logics, volume 10 of Trends in Logic. Kluwer, Dordrecht, 2001. J.G. Raftery: Order algebraizable logics. Annals of Pure and Applied Logic 164(3): 251-283, 2013. |