# Modal Logic (PH341-15)

## TIMING & CATS

This module is not running in 2017-18.

## MODULE DESCRIPTION

Modal operators are expressions such as it is necessary/possible that, in the future/past, it is obligatory/ permissible that, it is known/believed that, it is provable that, it is true after performing computational operation α that which when prefixed to a declarative sentence can be understood to modify the way in which it is true. Modal logic – i.e. the study of formal systems for reasoning about such operators – finds far reaching applications in philosophy, computer science, and mathematical logic.

We will begin studying axiom and tableau proof systems for some common propositional and first-order modal logics. We next consider a semantic theory for these systems in the form of Kripke (or possible world) models relative to which we will prove the soundness and completeness of the logics in question. Here are some topics we will touch on along the way: rigid designation and the de re/de dicto distinction (philosophy of language), possibilist versus actualist quantification (metaphysics), logical omniscience and bounded rationality (epistemology), intuitionism, formal versus informal provability and Gödel’s Incompleteness Theorems (mathematical logic), using modal logic to reason about distributed systems and program correctness (computer science).

## LEARNING OUTCOMES OR AIMS

By the end of the module the student should be able to: 1) demonstrate knowledge of formal systems of modal logic (proof theory and semantics); 2) understand the relationships between these formal systems and questions, e.g., about the nature of modality, identity, or conditionals; 3) use and define concepts with precision, both within formal and discursive context.

## CONTACT TIME

In this module students must attend 3 hours of lectures and a one hour seminar per week attended by all students.

Lectures for 2016-17

TBC

## ASSESSMENT METHODS

This module is formally assessed in the following way:

• Assessed exercises (15% of module)
• 2-hour examination (85% of module)