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Logic

Logic#

Overview#

This course introduces the logical foundations of automated reasoning as used in artificial intelligence: knowledge representation, the computation of logical consequence, and the main families of logics used to model the world (propositional, first-order, logic programming, modal, and description logics).

The thread running through the course is the central question of symbolic AI:

$$ KB \models \alpha \quad \text{(what can be inferred from a knowledge base?)} $$

and how it can actually be computed, a question progressively addressed in propositional logic, first-order logic, logic programming, and finally modal logic and description logics.

Outline#

  1. Foundations: representation, meaning, and entailment
  2. Propositional proof systems, resolution, and completeness
  3. Propositional reasoning as computation: chaining, DPLL, search
  4. First-order logic: syntax, semantics, and knowledge engineering
  5. Inference in first-order logic: Herbrand, unification, resolution
  6. Logic programming: SLD-resolution, Prolog, and Answer Set Programming
  7. Modal logic: possible worlds and Kripke semantics
  8. (If time permits) From modal logic to description logics: synthesis

In brief#

  • Period: semester 7
  • Credits: 3 ECTS
  • Number of hours: 24h
  • Apogée:
  • Discrete mathematics / basic set theory
  • Basic algorithms and complexity
  • Some programming ability

Pedagogical team#

  • Jérôme David

Evaluation#

Final exam + continous assessment