83 results on '"Bílková, Marta"'
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52. A Note on Uniform Interpolation Proofs in Modal Deep Inference Calculi
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Bílková, Marta, primary
- Published
- 2011
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53. Relation Liftings on Preorders and Posets
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Bílková, Marta, primary, Kurz, Alexander, additional, Petrişan, Daniela, additional, and Velebil, Jiří, additional
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- 2011
- Full Text
- View/download PDF
54. Proof Theory for Positive Logic with Weak Negation
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Bílková, Marta, primary and Colacito, Almudena, additional
- Published
- 2019
- Full Text
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55. The logic of resources and capabilities
- Author
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Greco, G., Bílková, Marta, Palmigiano, Alessandra, Tzimoulis, Apostolos, Wijnberg, Nachoem M., Greco, G., Bílková, Marta, Palmigiano, Alessandra, Tzimoulis, Apostolos, and Wijnberg, Nachoem M.
- Abstract
We introduce the logic LRC, designed to describe and reason about agents’ abilities and capabilities in using resources. The proposed framework bridges two—up to now—mutually independent strands of literature: the one on logics of abilities and capabilities, developed within the theory of agency, and the one on logics of resources, motivated by program semantics. The logic LRC is suitable to describe and reason about key aspects of social behaviour in organizations. We prove a number of properties enjoyed by LRC (soundness, completeness, canonicity, and disjunction property) and its associated analytic calculus (conservativity, cut elimination, and subformula property). These results lay at the intersection of the algebraic theory of unified correspondence and the theory of multitype calculi in structural proof theory. Case studies are discussed which showcase several ways in which this framework can be extended and enriched while retaining its basic properties, so as to model an array of issues, both practically and theoretically relevant, spanning from planning problems to the logical foundations of the theory of organizations.
- Published
- 2018
56. The logic of resources and capabilities
- Author
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LS Linguistiek de taalinformatica, UiL OTS LLI, Greco, G., Bílková, Marta, Palmigiano, Alessandra, Tzimoulis, Apostolos, Wijnberg, Nachoem M., LS Linguistiek de taalinformatica, UiL OTS LLI, Greco, G., Bílková, Marta, Palmigiano, Alessandra, Tzimoulis, Apostolos, and Wijnberg, Nachoem M.
- Published
- 2018
57. The Logic of Resources and Capabilities
- Author
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Bílková, Marta (author), Greco, G. (author), Palmigiano, A. (author), Tzimoulis, A. (author), Wijnberg, Nachoem (author), Bílková, Marta (author), Greco, G. (author), Palmigiano, A. (author), Tzimoulis, A. (author), and Wijnberg, Nachoem (author)
- Abstract
We introduce the logic LRC, designed to describe and reason about agents’ abilities and capabilities in using resources. The proposed framework bridges two—up to now—mutually independent strands of literature: the one on logics of abilities and capabilities, developed within the theory of agency, and the one on logics of resources, motivated by program semantics. The logic LRC is suitable to describe and reason about key aspects of social behaviour in organizations. We prove a number of properties enjoyed by LRC (soundness, completeness, canonicity, and disjunction property) and its associated analytic calculus (conservativity, cut elimination, and subformula property). These results lay at the intersection of the algebraic theory of unified correspondence and the theory of multitype calculi in structural proof theory. Case studies are discussed which showcase several ways in which this framework can be extended and enriched while retaining its basic properties, so as to model an array of issues, both practically and theoretically relevant, spanning from planning problems to the logical foundations of the theory of organizations., Ethics & Philosophy of Technology
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- 2018
- Full Text
- View/download PDF
58. Modal extensions of Ł_n-valued logics, coalgebraically
- Author
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Kurz, Alexander, Teheux, Bruno, and Bílková, Marta
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coalgebras ,Mathematics [G03] [Physical, chemical, mathematical & earth Sciences] ,Mathématiques [G03] [Physique, chimie, mathématiques & sciences de la terre] ,Łukasiewicz logic ,modal logic - Published
- 2017
59. THE LOGIC OF RESOURCES AND CAPABILITIES
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BÍLKOVÁ, MARTA, primary, GRECO, GIUSEPPE, additional, PALMIGIANO, ALESSANDRA, additional, TZIMOULIS, APOSTOLOS, additional, and WIJNBERG, NACHOEM, additional
- Published
- 2018
- Full Text
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60. Epistemic logics for sceptical agents
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Bílková, Marta, primary, Majer, Ondrej, additional, and Peliš, Michal, additional
- Published
- 2015
- Full Text
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61. Interpolace v modálních logikách
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Bílková, Marta, Pudlák, Pavel, Švejdar, Vítězslav, and Iemhoff, Rosalie
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Computer Science::Logic in Computer Science - Abstract
Since Craig's landmark result on interpolation for classical predicate logic, proved as the main technical lemma in [14], interpolation is considered one of the centra! concepts in pure logic. Various interpolation properties find their applications in computer science and have many deep purely logical consequences. We focus on two propositional versions of Craig interpolation property: Craig Interpolation Property: for every provable implication (A -+ B) there is an interpolant I containing only only common variables of A and B such that both implications (A -+ I) and (I-+ B) are provable. Craig interpolation, although it seems rather technical, is a deep logical property. It is dosely related to expressive power of a logic - as such it entails Beth's definability property, or forces functional completeness. It is also related to Robinson's joint consistency of two theories that agree on the common language. Craig interpolation has an important algebraic counterpart - it entails amalgamation or superamalgamation property of appropriate algebraic structures. In case of modal provability logics, Craig interpolation entails fixed point theorem. There are other interpolation properties, defined w.r.t. a consequence relation rather then w.r.t. a provable implication. In presence of deduction theorem the two...
- Published
- 2006
62. Epistemic logics for sceptical agents.
- Author
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BÍLKOVÁ, MARTA, MAJER, ONDREJ, and PELIŠ, MICHAL
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EPISTEMIC logic ,SEMANTICS (Philosophy) ,AXIOMS ,MULTIAGENT systems ,THEORY of knowledge - Abstract
In this article, we introduce an epistemic modal operator modelling knowledge over distributive non-associative full Lambek calculus with a negation. Our approach is based on the relational semantics for substructural logics: we interpret the elements of a relational frame as information states consisting of collections of data. The principal epistemic relation between the states is the one of being a reliable source of information, on the basis of which we explicate the notion of knowledge as information confirmed by a reliable source. From this point of view it is natural to define the epistemic operator formally as the backward-looking diamond modality. The framework is a generalization and extension of the system of relevant epistemic logic proposed by Majer and Peliš (2009, college Publications, 123-135) and developed by Bílková et al. (2010, college Publications, 22-38). The system is modular in the sense that the axiomatization of the epistemic operator is sound and complete with respect to a wide class of background logics, which makes the system potentially applicable to a wide class of epistemic contexts. Our system admits a weak form of logical omniscience (the monotonicity rule), but avoids stronger ones (a necessitation rule and a K-axiom) as well as some closure properties discussed in normal epistemic logics (like positive and negative introspection). For these properties we provide characteristic frame conditions, so that they can be present in the system if they are considered to be appropriate for some specific epistemic context.We also prove decidability of the weakest epistemic logic we consider, using a filtration method. Finally, we outline further extensions of our framework to a multiagent system. [ABSTRACT FROM AUTHOR]
- Published
- 2016
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63. On monotone modalities and adjointness
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BÍLKOVÁ, MARTA, primary, VELEBIL, JIŘÍ, additional, and VENEMA, YDE, additional
- Published
- 2011
- Full Text
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64. Interpretability in PRA
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Bílková, Marta, primary, de Jongh, Dick, additional, and Joosten, Joost J., additional
- Published
- 2009
- Full Text
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65. Proof theory for positive logic with weak negation
- Author
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Bílková, Marta and Colacito, Almudena
- Subjects
TheoryofComputation_MATHEMATICALLOGICANDFORMALLANGUAGES ,510 Mathematics ,TheoryofComputation_LOGICSANDMEANINGSOFPROGRAMS ,Computer Science::Logic in Computer Science ,16. Peace & justice - Abstract
Proof-theoreticmethods are developed for subsystems of Johansson’s logic obtained by extending the positive fragment of intuitionistic logic with weak negations. These methods are exploited to establish properties of the logical systems. In particular, cut-free complete sequent calculi are introduced and used to provide a proof of the fact that the systems satisfy the Craig interpolation property. Alternative versions of the calculi are later obtained by means of an appropriate loop-checking history mechanism. Termination of the new calculi is proved, and used to conclude that the considered logical systems are PSPACE-complete.
66. Aspects of the Cut-Elimination Theorem
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Rýdl, Jiří, Švejdar, Vítězslav, and Bílková, Marta
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cut rule|sequent calculus|lengths of proofs ,pravidlo řezu|sekventový kalkulus|délky důkazů - Abstract
I give a proof of the cut-elimination theorem (Gentzen's Hauptsatz ) for an intuitionistic multi-succedent calculus. The proof follows the strategy of eliminating topmost maximal-rank cuts that allows for a straightforward way to measure the upper bound of the increase of derivations during the procedure. The elimination of all cut inferences generates a superexponential increase. I follow the structure of the proof for classical logic given in Švejdar's [18], modifying only the critical cases related to two restricted rules. Motivated by the diversity found in the early literature on this topic, I survey selected aspects of various formulations of sequent calculi. These are reflected in the proof of the Hauptsatz and its preliminaries. In the end I give one corollary of cut elimination, the Midsequent theorem, which is one of the three applications to be found already in Gentzen's [10].
- Published
- 2021
67. Usuzování s nekonzistentními informacemi
- Author
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Přenosil, Adam, Bílková, Marta, Noguera, Carles, and Jansana, Ramon
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TheoryofComputation_MATHEMATICALLOGICANDFORMALLANGUAGES ,TheoryofComputation_LOGICSANDMEANINGSOFPROGRAMS ,Computer Science::Logic in Computer Science ,abstraktní algebraická logika|Belnapova-Dunnova logika|parakonzistentní logika|superbelnapovské logiky ,abstract algebraic logic|Belnap-Dunn logic|paraconsistent logic|super-Belnap logics ,Hardware_LOGICDESIGN - Abstract
This thesis studies the extensions of the four-valued Belnap-Dunn logic, called super-Belnap logics, from the point of view of abstract algebraic logic. We describe the global structure of the lattice of super-Belnap logics and show that this lattice can be fully described in terms of classes of finite graphs satisfying some closure conditions. We also introduce a theory of so- called explosive extensions and use it to prove new completeness theorems for super-Belnap logics. A Gentzen-style proof theory for these logics is then developed and used to establish interpolation for many of them. Finally, we also study the expansion of the Belnap-Dunn logic by the truth operator ∆. Keywords: abstract algebraic logic, Belnap-Dunn logic, paraconsistent logic, super-Belnap logics
- Published
- 2018
68. Fragmenty intuicionistické logiky, intermediárích logik a substrukturálních logik (vybrané otázky)
- Author
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Truhlář, Pavel, Bílková, Marta, and Sedlár, Igor
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substrukturální logiky|rámce|pozitivní formule|top model|slabý zákon vyloučeného třetího ,substructural logics|frames|positive formulas|top model|weak excluded middle axiom ,Computer Science::Logic in Computer Science - Abstract
The abstract of the diploma thesis "Positive Formulas for Some Substructural Logics" by Pavel Truhlar We will examine which distributive substructural logics, as defined in the book of Restall "An Introduction to Substructural Logics" have the same positive fragment with and without the weak excluded middle axiom. The main result of this diploma thesis is that some substructural logics have this property. We repeat the basic notions as described in the Restall's book, especially the consecution, natural deduction, frame semantics, Hilbert system. We will use the soundness and completeness theorems. We also will use the equivalence of natural deduction systems and Hilbert systems. All these important theorems are in the above mentioned Restall's book. We make the proof of our main result in the next part. We will use the semantics of frames, similarly as de Jongh and Zhao in the article "Positive Formulas in Intuitionistic and Minimal Logic". We will define the top model. After, we define the construction which converts a model to the top model. We define for each formula the positive part of it; this is the formula, which behaves the same way on the top models as the original formula. We use Hilbert type calculus to formulate our main theorem. We prove our main result using the deduction theorem for certain...
- Published
- 2018
69. Hypothetical Judgements, Truth and Assertibility
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Punčochář, Vít, Kolman, Vojtěch, Sedlár, Igor, and Bílková, Marta
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intuitionistic logic ,pragmatika ,Kondicionální věty ,inkvizitivní sémantika ,inquisitive semantics ,assertibility ,tvrditelnost ,sémantika ,intuicionistická logika ,truth ,pravdivost ,pragmatics ,semantics ,Conditionals - Abstract
Vít Punčochář Dissertation: Hypothetical Judgements, Truth and Assertibility Abstract: The main topic of this thesis is the logic of indicative conditionals, i.e. sentences of the form If A then B. In classical logic, these sentences are analysed with the help of the so- called material implication. However, the analysis is problematic in many respects. Some chapters of the thesis are devoted to the explanation of the problems, which one necessarily faces when analysing conditionals with the apparatus of standard classical logic. The stress is laid upon the fact that here we are led to a paradoxical situation: some general principles of classical logic (e.g. the principle according to which one can infer If not-A then B from A or B) seem to be unquestionable, but they have very controversial consequences. In the thesis, attempts are presented to defend classical logic as well as to revise it. The approaches to the logical analysis of conditionals are classified into two basic kinds: the first one might be called ontic and the second one epistemic. The ontic approach defines all crucial semantic notions in terms of the concept of truth that is modelled in logic as a relation between sentences of a given language and states of affairs. In contrast, the epistemic approach is not based on the concept of truth...
- Published
- 2016
70. Nerozhodnutelnost některých substrukturálních logik
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Chvalovský, Karel, Bílková, Marta, Buszkowski, Vojciech, and Galatos, Nick
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TheoryofComputation_MATHEMATICALLOGICANDFORMALLANGUAGES ,Computer Science::Logic in Computer Science ,undecidability ,sequent calculi ,substructural logics ,provability ,nerozhodnutelnost ,substrukturální logiky ,dokazatelnost ,sekventové kalkuly - Abstract
This thesis deals with the algorithmic undecidability (unsolvability) of provability in some non-classical logics. In fact, there are two natural variants of this problem. Fix a logic, we can study its set of theorems or its consequence relation, which is a more general problem. It is well-known that both these problems can be undecidable already for propositional logics and we provide further examples of such logics in this thesis. In particular, we study propositional substructural logics which are obtained from the sequent calculus LJ for intuitionistic logic by dropping structural rules. Our main results are the following. First, (finite) consequence relations in some basic non-associative substructural logics are shown to be undecidable. Second, we prove that a basic associative substructural logic with the contraction rule, which is notorious for being hard to handle, has an undecidable set of theorems. Since the studied logics have natural algebraic semantics, we also obtain corresponding algebraic results which are interesting in their own right.
- Published
- 2015
71. Arithmetical completeness of the logic R
- Author
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Holík, Lukáš, Švejdar, Vítězslav, and Bílková, Marta
- Subjects
modal logics ,rosserovské modality ,pevný bod ,Provability logic ,Logika dokazatelnosti ,modální logiky ,Rosser modalities ,fixed point - Abstract
The aim of this work is to use contemporary notation to build theory of Rosser logic, explain in detail its relation to Peano arithmetic, show its Kripke semantics and finally using plural self-reference show the proof of arithmetical completeness. In the last chapter we show some of the properties of Rosser sentences. Powered by TCPDF (www.tcpdf.org)
- Published
- 2014
72. Čtyřhodnotová sémantika klasické a intuicionistické logiky
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Přenosil, Adam, Bílková, Marta, and Cintula, Petr
- Subjects
Mathematics::Logic ,de Morgan algebras ,duality ,čtyřhodnotová logika ,de Morganovské algebry ,neklasická logika ,four-valued logic ,non-classical logic ,teorie důkazů ,dualita ,proof theory ,Computer Science::Logic in Computer Science - Abstract
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)
- Published
- 2013
73. Dynamické epistemické logiky
- Author
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Pivoňková, Martina, Bílková, Marta, and Sedlár, Igor
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TheoryofComputation_MATHEMATICALLOGICANDFORMALLANGUAGES ,logika přesvědčení ,logic for belief ,public announcement logic ,logika veřejného prohlášení ,ComputingMilieux_MISCELLANEOUS - Abstract
In this thesis we will deal with the logic of public announcement which is a dynamic extension of epistemic logic. First we will explain the logic of truthful public announcement for the multiagent S5 system. Then we will examine what the public announcement can look like in systems weaker than S5. We will focus namely on systems in which the T axiom is invalid and the epistemic modality is interpreted not as a "knowledge" but as a "belief". We will create new semantics of public announcement which is not necessarily truthful but it is believed to be true. We will also try to axiomatize systems that have arisen in this way. Keywords: public announcement logic, logic for belief
- Published
- 2012
74. Algebraická a kripkovská sémantika substrukturálních logik
- Author
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Arazim, Pavel, Bílková, Marta, and Běhounek, Libor
- Subjects
category ,kripkovské rámce ,distributive residuated lattice ,distributive full Lambek calculus ,distributivní logika FL ,functor ,frame morphisms ,distributive FL logic ,funktor ,structural rules ,distributivní residuované svazy ,strukturální pravidla ,kategorie ,distributivní Lambekův kalkul ,morfismy mezi rámci ,Kripke frames ,Mathematics::Category Theory ,Computer Science::Logic in Computer Science ,Computer Science::Programming Languages - Abstract
This thesis is about the distributive full Lambek calculus, i.e., intuicionistic logic without the structural rules of exchange, contraction and weakening and particularly about the two semantics of this logic, one of which is algebraic, the other one is a Kripke semantic. The two semantics are treated in separate chapters and some results about them are shown, for example the disjunction property is proven by amalgamation of Kripke models. The core of this thesis is nevertheless the relation of these two semantics, since it is interesting to study what do they have in common and how can they actually differ, both being a semantics of the same logic. We show how to translate frames to algebras and algebras to frames, and, moreover, we extend such translation to morphisms, thus constructing two functors between the two categories. Key words:distributive FL logic, distributive full Lambek calculus, structural rules, distributive residuated lattice, Kripke frames, frame morphisms, category, functor 2
- Published
- 2011
75. Proofs in natural deduction and sequent system in substructural logic FL
- Author
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Dolejší, Zuzana, Bílková, Marta, and Běhounek, Libor
- Subjects
Gentzenovský kalkul ,Substructural logics ,Odvození ,Full Lambek ,Gentzen Calculus ,Natural Deduction Calculus ,Důkaz ,Derivation ,Kalkul Přirozené dedukce ,Substrukturální logiky ,Proof - Published
- 2011
76. Intuicionistická logika jako užitečný nástroj
- Author
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Vachková, Eva, Švejdar, Vítězslav, and Bílková, Marta
- Subjects
Mathematics::Logic ,TheoryofComputation_MATHEMATICALLOGICANDFORMALLANGUAGES ,TheoryofComputation_LOGICSANDMEANINGSOFPROGRAMS ,Computer Science::Logic in Computer Science - Abstract
This work deals with intuitionistic logic and completness of Gentzen calculus with respect to its semantics. The completness proof uses saturated sequents. The language considered is at most countable. Furthermore, our work investigates one of the generalizations of intuitionistic logic, namely intuitionistic logic with constant domain, or Grzegorczyk's logic. We deal with Markov's principle and use it to prove that Gentzen calculus adapted to this logic is not cut-free complete with respect to Grzegorczyk's logic. Part of the work deals with Heyting algebras-one of the possible semantics of intuitionistic propositional logic. We show that the Rieger-Nishimura lattice is a Heyting algebra, too. For Heyting algebras, filters and prime filters are defined and used to obtain Kripke's frames. It is shown that the same formulas hold in these frames and in Heyting algebras.
- Published
- 2010
77. Sémantika některých neobvyklých modálních logik
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Punčochář, Vít, Bílková, Marta, and Peregrin, Jaroslav
- Subjects
TheoryofComputation_MATHEMATICALLOGICANDFORMALLANGUAGES - Abstract
The rst part deals with Carnap s contribution to the modal logic. The Carnap s work is included in the historical context. His reaction to the Lewis calculi of the strict implication is discussed and also his anticipation of the Kripkean possible worlds semantics, which the contemporary modal logic is based on. The main aim of the second part was to consider some kinds of modalities. These kinds of modalities have epistemic character because they always depend on certain knowledge. The main result of the diploma work is the introduction of four new logics. Their semantics is set up in the similar fashion in which Carnap de ned his own modal logic. Some basic features of these logics are shown and their axiomatization and relationship to some other more usual logics is investigated.
- Published
- 2009
78. Kategorie fuzzy množin
- Author
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Luhan, Ondřej, Bílková, Marta, and Běhounek, Libor
- Subjects
Mathematics::Category Theory - Abstract
Category theory provides very useful tools for studying mathematical structures and phenomena. One of the structures that is studied in a category-theoretical manner are fuzzy sets. If we consider fuzzy sets as objects and set up certain kind of structure preserving mappings as morphisms, we can obtain a suitable category for our purposes. Goal of this work is to give an overview of preferably all important category-theoretical approaches to fuzzy sets that were done throughout relatively short history of category-theoretical modelling of fuzzy sets.
- Published
- 2009
79. Tableaux in non-classical logics
- Author
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Dančák, Michal, Peliš, Michal, and Bílková, Marta
- Abstract
Dalo by se ríct, že jako dukazová metoda jsou sémantické stromy v Cesku nepríliš používané, a to i presto, že ve svete je to nejoblíbenejší dukazový systém pro modální logiku [1]. Vedle základního Hilbertova kalkulu se v ceské literature nejcasteji objevují sekventové kalkuly, prípadne kalkul prirozené dedukce. Presto má metoda sémantických stromu nekolik nezanedbatelných predností a zajímavých témat. Jak už název napovídá, tento kalkul vychází ze sémantiky - dukazy mají predevším sémantický charakter a pro "jednodušší" logiky jsou i velmi intuitivní. Dokazování je zároven i vyvracení. Pri dokazování metodou sémantických stromu vlastne hledáme protipríklad. Jestliže ho nenajdeme, a pokud jsme postupovali správne, tak neexistuje. Na poradí použití pravidel také nezáleží (až na nekolik vyjímek v nekterých logikách, které si pozdeji ukážeme). I díky temto výhodám je tato metoda také velmi vhodná pro strojové zpracování. V této práci jsem se rozhodl zamerit na to, jak se metoda sémantických stromu chová v substrukturální logice BCK (nekdy též FLew). Zacneme základními definicemi a tím, co to vlastne sémantické stromy jsou, dále bude následovat nekolik príkladu, definice logiky BCK a príslušných odvozovacích pravidel. Celá práce bude završena dukazem úplnosti a korektnosti tohoto kalkulu vuci kripkovské...
- Published
- 2009
80. Relace bisimulace
- Author
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Arazim, Pavel, Švejdar, Vítězslav, and Bílková, Marta
- Subjects
TheoryofComputation_MATHEMATICALLOGICANDFORMALLANGUAGES ,TheoryofComputation_LOGICSANDMEANINGSOFPROGRAMS - Abstract
This work is about bisimulation in modal logic as well as in intuicionistic logic without contraction. Bisimulation is a relation between models, which is weaker than isomorphism, yet still guarantees equivalence in the in the selected logic. It is typically used to demonstrate that some properties of models cannot be distinguished. For instance the cardinality cannot be distinguished, which is shown by disjunct union. Bisimulation also helps to clarify the relation between modal and classical logic. Apart from bisimulation, the related notion of bounded morphism is studied because it enables to elevate the unde- nability and undistinguishability to the discourse of frames. The part about modal logic is basically a compilation of well known facts, yet their interaction is made more clear and some proofs, which are usually disregarded as obvious, are presented in an explicit manner. Talking about the second part, mere reasonable de nition of the semantics is an honest work. Yet even here the bisimulation and bounded isomorphism are introduced and some examples are shown in order to illustrate their utility.
- Published
- 2009
81. Mutual comparison of modal logics axiomatic system
- Author
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Pelikán, David, Jirků, Petr, and Bílková, Marta
- Abstract
Tato diplomová práce se zabývá modálními logikami z formálního pohledu. Jsou v ní de novány základní formální systémy a jsou předvedeny hlavní vztahy mezi nimi.
- Published
- 2008
82. Explicit fixed-points in provability logic
- Author
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Chvalovský, Karel, Švejdar, Vítězslav, and Bílková, Marta
- Abstract
The aim of this diploma thesis is to discuss the explicit calculations of xed-points in provability logic GL. The xed-point theorem reads: For every modal formula A(p) such that each occurrence of p is under the scope of ¤, there is a formula D containing only sentence letters contained in A(p), not containing the sentence letter p, such that GL proves D ' A(D). Moreover, D is unique up to the provable equivalence. Firstly, we establish some special cases of the theorem and then we will look more closely at the full theorem. We show one semantic and two syntactic full xed-point constructions and prove their correctness. We also discuss some complexity aspects connected with the constructions and present basic upper bounds on length and modal depth of the constructed xed-points.
- Published
- 2007
83. Fuzzification of simple systems of deontic logic
- Author
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Vostrá, Nelly, Bílková, Marta, and Běhounek, Libor
- Abstract
Deontické logiky bývají formalizovány jako druh modálních logik. V této práci aplikuji fuzzy modální logiku na dvojí systémy monadick ých deontických logik - systémy deontické logiky v užším smyslu a systémy alethické logiky s výrokovou konstantou Q. Pro tyto nové fuzzy deontické logiky dokazuji lokální větu o dedukci, korektnost vřuči příslušným fuzzy rámcřum a definovatelnost deontick ých systémřu v alethických.
- Published
- 2006
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