Aktivitet: Foredrag og mundtlige bidrag › Foredrag og præsentationer i privat eller offentlig virksomhed
This course is mainly addressed to postgraduate students in Computer Science and Mathematics with the aim of introducing the basic concepts, results and tools from Mathematical Logic and Model Theory. The course will approach most of the hot problems in these fields, from the paradoxes of Set Theory to Gödel's theorems, while the main focus will be on Classical First and Second Order Logics and on Modal Logics. We will formally define various metamathematical concepts such as syntax, semantics, truth, provability, completeness and complete axiomatizations, compactness, decidability, quantification etc. With some of these concepts the students are already familiar from more specific courses. The role of this course is to present these concepts in a general framework and to clarify the spectrum of their use and applicability.
Formally, the course will cover the following topics:
I. An introduction to Classical Logic and Model Theory I.1. Formal Theories I.2. Propositional Logic (PL) I.2.1 Syntax and Semantics, truth tables I.2.2 Conjunctive and disjunctive normal forms I.2.3 Proof theories for PL I.2.4. Completeness and compactness I.3. First Order Logic (FOL) I.3.1. Syntax and Semantics I.3.2. Axiomatization I.3.3. Completeness and Compactness I.3.4. Lowenheim-Skolem Theorems I.3.5. Henkin’s constants and the relation to PL I.4. Monadic Second Order Logic and finite state machines
II. Modal Logic and its Model Theory II.1. Kripke structures and transition systems II.2. Bisimulations and zig-zag morphisms II.3. The standard translation into FOL and SOL II.4. Model constructions II.5. Bisimulation and invariance II.6. Classical truth-preserving constructions II.7. Axiomatizations and Weak Completeness II.7.1. Axiomatic systems II.7.2. Finite model property II.7.3. Canonical models II.7.4. The filtration method
III. Multimodal Logics for Transition Systems III.1. Hennessy-Milner Logic III.2. Dynamic Logic III.3. Epistemic Logics III.4. Probabilistic and Markovian Logics III.5. Temporal and probabilistic/stochastic temporal logics