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d-Frames as algebraic duals of bitopological spaces
Jakl, Tomáš ; Pultr, Aleš (advisor) ; Picado, Jorge (referee) ; Cintula, Petr (referee)
Achim Jung and Drew Moshier developed a Stone-type duality theory for bitopological spaces, amongst others, as a practical tool for solving a particular problem in the theory of stably compact spaces. By doing so they discovered that the duality of bitopological spaces and their algebraic counterparts, called d-frames, covers several of the known dualities. In this thesis we aim to take Jung's and Moshier's work as a starting point and fill in some of the missing aspects of the theory. In particular, we investigate basic categorical properties of d-frames, we give a Vietoris construction for d-frames which generalises the corresponding known Vietoris constructions for other categories, and we investigate the connection between bispaces and a paraconsistent logic and then develop a suitable (geometric) logic for d-frames.
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A Four-Valued Kripke Semantics for Classical and Intuitionistic Logic
Přenosil, Adam ; Bílková, Marta (advisor) ; Cintula, Petr (referee)
The thesis introduces a logic which combines intuitionistic implication with de Morgan negation in a way which conservatively extends both classical and intuitionistic logic. This logic is the intuitionistic counterpart of the four-valued Belnap-Dunn logic. In relation to this logic, we study de Morgan algebras and their expansions, in particular their expansion with a constant representing inconsistency. We prove a duality for such algebras extending the Priestley duality. We also introduce a weak notion of modal algebra and prove a duality for such algebras. We then define analytic sequent calculi for various logics of de Morgan negation. Powered by TCPDF (www.tcpdf.org)
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NCMPL 2011 Abstracts
Cintula, Petr ; Ju, S. ; Víta, Martin
This volume contains (extended) abstracts of all 6 invited and 25 contributed talks presented at the conference Non-Classical Modal and Predicate Logics which took place in Guangzhou, December 5-9, 2011. Modalities and predicates have since ancient time been central notions in logic. In the 20th century, various systems of non-classical logics have emerged, with applications in many disciplines like Computer Science, Linguistics, Mathematics, and Philosophy. This gave rise to the questions of non-classical treatment of quantification and modalities and their accommodation in these non-classical settings. In response, various modal and predicate variants of non-classical logics have been introduced and studied in the past decades. Although there are many good conferences on (mainly propositional) non-classical logics, this conference was solely dedicated to modal and predicate non-classical logics. Its aim was to bring together esearchers from various branches of non-classical logics, not only to present recent advances in their particular fields, but also to identify common problems and methods and foster the exchange of ideas between researchers from separate fields.
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Logic, Algebra and Truth Degrees 2010
Chvalovský, Karel ; Cintula, Petr ; Noguera, C.
Volume of abstracts from the conference Logic, Algebra and Truth Degrees 2010 (the second official meeting of the EUSFLAT Working Group on Mathematical Fuzzy Logic) which was held on 7-11 September 2010 in Prague. The volume was published by Institute of Theoretical informatics as volume 2010-502 of ITI Series and is available at http://iti.mff.cuni.cz/series/
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Fuzzy teorie tříd: některá pokročilá témata
Cintula, Petr ; Horčík, Rostislav
The goal of this paper is to push forward the development of the apparatus of the Fuzzy Class theory. We concentrate on three areas: strengthening the universal quantifier, formalizing the idea that `similar' fuzzy sets fulfill their properties to `similar' degrees, and embedding of classical crisp theories into Fuzzy Class theory.
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