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Lecturer(s)
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Course content
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(1) Definition of logical inference (2) Semantics of propositional logic (ProL) (3) Semantic proof in ProL (4) Syntactic proof in ProL (5) Semantics of first-order predicate logic (PreL1) (6) Models of PreL1 formulas (7) Semantic proof in PreL1: a) Venn diagram method b) relational structures (8) Completeness vs. correctness of calculus (9) Proof in theories (10) Theories of relational structures (11) Algebraic theories
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Learning activities and teaching methods
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Lecture, Dialogic Lecture (Discussion, Dialog, Brainstorming)
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Learning outcomes
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The course deals with logical semantics of propositional logic and first-order predicate logic. It is conceived so that the issues can be comprehended even by students who have no prior experience with logic. To begin with, logic will be introduced, with its subject matter and definition of logical inference. Students will then be acquainted with formalism and semantics of propositional logic (ProL) and first-order predicate logic (PreL1). With the issue of semantics (that is to say, meaning of formulas) of propositional and predicate logic, theory of models that forms its foundations will be introduced. The difference between semantic and syntactic proof will be demonstrated. From semantic proof methods for ProL the table method will be presented, as well as proof by contradiction. In case of semantic methods for PreL1, the method of Venn diagram and relational structures will be presented. From semantic proof methods for ProL and PreL1, resolution method and natural deduction method will be presented. Finally, students will be introduced to the issue of formalized theories and proof in theory.
Students will then be acquainted with formalism and semantics of propositional logic (ProL) and first-order predicate logic (PreL1), gaining ability to find models of formulas of ProL and PreL1. They will gain knowledge of methods of performing syntactic and semantic proof in ProL and PreL1 and will be able to use these methods to prove validity of judgements.
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Prerequisites
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unspecified
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Assessment methods and criteria
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Written exam
(1) Regular presence (no more than 2 unexcused absences) (2) Completion of three in-class tests with score of 50% or more (3) Score of 70% or more in the final test
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Recommended literature
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Duží, M. (2012). Logika pro informatiky a příbuzné obory. Ostrava.
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Janák, V. (1974). Základy formální logiky.. Praha: SPN.
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Priest, G. (2007). Logika.. Praha: Dokořán.
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Smullyan, M. R. (2004). Satan, Cantor a nekonečno. Praha.
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Svoboda, V. - Peregrin, J. (2009). Od jazyka k logice. Praha.
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Svoboda, V. a kol. (2010). Logika a přirozený jazyk. Praha.
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Štěpán, J. (1995). Formální logika. Olomouc : FIN.
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