Modal and temporal logic in artificial intelligence

Davide Bresolin
Dipartimento di Matematica, Università degli Studi di Padova,


Formal logic has had a central place in the study of artificial intelligence since its first conception in the 1950s. Why is this so? Logic has not been made formal just to make it suitable for computers and robots. Formal logic is also a tool for humans. Just as we could write, and execute, our grocery list and daily schedules in a computer program, so we could make our daily inferences by means of deduction in formal logic. Moreover, formal logic wasn’t even invented for machines, but to regiment and explicate human scientific reasoning.

The course will give an introduction to modal logic and temporal logic for students of the BMCS doctoral program. It will give the basics facts about modal and temporal logic, to provide a common ground for further study. Then, it will show why modal and temporal logics have become over the past 50 years very useful and important in computer science, and particularly for the formal specification, verification and synthesis of computerised systems of various nature


- Brief history and philosophical origins of modal and temporal logic.
- The basic modal logic K. Relational (possible worlds) semantics. Truth and validity of modal formulae.
- Reasoning about knowledge and beliefs: epistemic modal logic.
- Applications of epistemic logic in cognitive sciences.
- Reasoning about time. Linear time and branching time temporal logics.
- Applications of temporal logic in computer science: specification, verification and synthesis of reactive systems.

Introductory reading
Ahti-Veikko Pietarinen. 2003. What do epistemic logic and cognitive science have to do with each other?. Cogn. Syst. Res. 4, 3 (September 2003), 169-190.

Course requirements
The course does not presuppose any previous background in formal logic nor in artificial intelligence.

Examination modality

Course material, enrollment and last minute notifications
Made available by the teacher at this Moodle address

6 May 2019, 14:30-16:30
7 May 2019, 14:30-16:30
8 May 2019, 14:30-16:30

Meeting room 702, 7th floor, Dept of Mathematics

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