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Introspection of Vague Knowledge in Fuzzy Logic
Běhounek, Libor
In classical epistemic logic, the principle of introspection for vague knowledge is precluded by Poincaré's paradox, which implies that the relation of indistinguishability cannot be transitive. The paper shows that the introspection principle for vague knowledge can be saved if T-transitive indistinguishability relations in fuzzy logic are used.
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Two Connections between Epistemic and Fuzzy Logics
Běhounek, Libor
Two possible connections between epistemic and fuzzy logics are studied. Epistemic fuzzy logic as a kind of modal logic studies the reasoning of agents about fuzzy propositions; problems of such a synthesis caused by the invalidity of the axiom K are hinted at. Another direction is to found epistemic on fuzzy logic; the paper sketches the way how representing feasible knowledge as a fuzzy modality eliminated the logical omniscience paradox.
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Relativní interpretace v prvořádové fuzzy logice.
Běhounek, Libor
The classical notion of relative interpretation (also known as a direct syntactic model) is adapted for multi-sorted first-order fuzzy logics. The level of generality is chosen to suit the needs of its applications in Fuzzy Class Theory.
Fulltext: content.csg - PDF Plný tet: 0042506 - PDF
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Kurt Goedel - life, results and their significance
Běhounek, Libor
A survey (in Czech) of K. Gödel’s most important results and works in metamathematics, set theory, physics, and philosophy. A special attention is given to de-mything Gödel’s Incompleteness Theorems and to their consequences for computer science, artificial intelligence, philosophy, and other disciplines.
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Fuzzy Macneillovské a Dedekindovské zúplnění ostrých lineárních hustých uspořádání
Běhounek, Libor
In the framework of Henkin-style higher-order fuzzy logic we devone two kinds of the fuzzy lattice completion. The fuzzy MacNeille completion is the lattice completion by (possibly fuzzy) stable sets; the fuzzy Dedekind completion is the lattice completion by (possibly fuzzy) Dedekind cuts. We investigate the properties and interrelations of both notions and compare them to the results from the literature. Our attention is restricted to crisp dense linear orderings, which are important for the theory of fuzzy real numbers.
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Dva pojmy fuzzy svazového zúplnění
Běhounek, Libor
In the framework of Henkin-style-order fuzzy logic we define two notions of fuzzy lattice completion. Out attention is restricted to dense linear crisp orderings, which are important for the theory of fuzzy real numbers. We investigate the properties of both notions and compare them with some results from the literature.
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