Logic
Propositional Calculus: the notion of formal language. Formal language of propositional calculus. Translations. Inductive definitions and recursive definitions. The semantics of propositional language. The notion of logical consequence. Algebra of propositions. The Natural Deduction system for Classical logic. Calculation of Predicates: the formal language of calculating first order predicates. Semantics for first order language. Definability, homomorphisms between structures. The Natural Deduction system for classical First Order logic.
Mandatory:
- Enderton, H. B. (2000). A Mathematical Introduction to Logic (2nd ed.). Harcourt / Academic Press.
- van Dalen, D. (2004). Logic and Structure. Springer.
- Goldblatt, R. (1987). Logics of Time and Computation. University of Chicago Press.
Complementary:
- Brachman, R., & Levesque, H. (2004). Knowledge Representation and Reasoning. The Morgan Kaufmann Series in Artificial Intelligence (1st ed.). Morgan Kaufmann.
- Mates, B. (1972). Elementary Logic. Oxford University Press.
- Velleman, D. J. (2006). How to Prove It: A Structured Approach. Cambridge University Press.
- Jr., E. M. C., Grumberg, O., & Peled, D. A. (1999). Model Checking. MIT Press.