Nonclassical models of reasoning - ALG519025

• Title: Nonclassical models of reasoning
• Guaranteed by: Department of Logic (21-KLOG)
• Faculty: Faculty of Arts
• Actual: from 2023
• Semester: both
• Points: 0
• E-Credits: 6
• Hours per week, examination: 2/1, Ex [HT]
• Capacity: winter:unknown / unknown (unknown); summer:unknown / unknown (unknown)
• Min. number of students: unlimited
• 4EU+: no
• Virtual mobility / capacity: no
• State of the course: taught
• Language: English, Czech
• Teaching methods: full-time
• Teaching methods: full-time
• Note: course can be enrolled in outside the study plan; enabled for web enrollment; you can enroll for the course in winter and in summer semester
• Guarantor: Mgr. Marta Bílková, Ph.D.; RNDr. Zuzana Haniková, Ph.D.
• Teacher(s): RNDr. Zuzana Haniková, Ph.D.

Annotation

Last update: Mgr. Šárka Stejskalová, Ph.D. (20.02.2024)

The course is a survey of some well-known families of nonclassical logics, studied using mathematical methods.

Literature

Last update: Mgr. Šárka Stejskalová, Ph.D. (20.02.2024)

Nikolaos Galatos, Peter Jipsen, Tomasz Kowalski, Hiroakira Ono: Residuated Lattices: An Algebraic Glimpse at Substructural Logics. Vol. 151 Studies in Logics and the Foundations of Mathematics, Elsevier,2007.
Petr Hájek: Metamathematics of Fuzzy Logic. Kluwer, 1998.
P. Cintula, P. Hájek, C. Noguera (eds.): Handbook of Mathematical Fuzzy Logic. vol. 37,38 Mathematical Logic and Foundations, College Publications, 2011.
Hilary A. Priestley, Brian A. Davey: Introduction to Lattices and Order. Cambridge University Press, 1990, 2002.
Alexander Chagrov and Michael Zakharyaschev, Modal Logic, vol. 35 of Oxford Logic Guides, Oxford University Press, 1997.
Patrick Blackburn, Maarten de Rijke, Yde Venema: Modal Logic. Cambridge University Press, 2001.
Christos H. Papadimitriou: Computational complexity. Addison-Wesley, 1994.

Syllabus

Last update: Mgr. Šárka Stejskalová, Ph.D. (20.02.2024)

1. Intuitionism, intuitionistic logic. Calculi, relational and algebraic semantics. The lattice of superintuitionistic logics. Decision procedures and complexity.
2. Modal logics. Modal companions. Standard translation into classical logic. Complexity.
3. Lambek calculus, Full Lambek calculus, the lattice of substructural logics. Residuated lattices. Fuzzy logics.
4. Arithmetic and set theory in a nonclassical setting. Some applications of nonclassical logics.