1. komponenta

Lecture type	Total
Lectures	45

* Load is given in academic hour (1 academic hour = 45 minutes)

COURSE AIMS AND OBJECTIVES:
The course goal is to introduce a basic of propositional modal logic. Modal logic is considered as a language for describing relational structures. The accent is on the study Kripke semantics.

COURSE DESCRIPTION AND SYLLABUS:
1. Syntax and semantics of modal and temporal logic. Relational structures. Transition systems. Modal languages. Basic modal language. Basic temporal language. Models and frames. Two-way frames. General frameworks. Modal relations of logical consequence. Normal modal logic.
2. Basic model constructions. Disjunctive unions. Generated submodels. Limited morphisms. Bisimulations. Temporal bisimulations. Property of finite models. Standard translation. Modal definability. Definable and indefinable properties of relational structures
3. Soundness and completeness. Canonical models. Completeness of modal systems. Completeness of basic temporal logic.
4. Decidability and complexity. The problem of satisfiability and validity. Decidability using the properties of finite models. Complexity of algorithms for validity problems of modal formulas. Examples of application in specification and verification.
5. Extensions of modal and temporal logic. Temporal logic extended by Since and Until operators. Linear temporal logic LTL. Temporal logics with branching CTL * and CTL. Hybrid logic.

1. Modal Logic, P. Blackburn, M. de Rijke, Y. Venema, Elsevier, 2001.
2. Handbook of Modal Logic, P. Blackburn, J. van Benthem, F. Wolter i dr. (ur.), Elsevier, 2006.
3. Temporal logics in computer science: finite-state systems, S. Demri, V. Goranko, M. Lange, Cambridge University Press, 2016.
4. Matematička logika, M. Vuković, Element, Zagreb, 2009.

Enrollment :
Attended : Mathematical logic

Examination :
Passed : Mathematical logic

Ostali izborni predmeti - Regular study - Computer Science and Mathematics
Vezani kolegiji B - Regular study - Computer Science and Mathematics

Ostali izborni predmeti - Regular study - Computer Science and Mathematics
Vezani kolegiji B - Regular study - Computer Science and Mathematics