Logic for Computer Science and Artificial Intelligence

Chapter 10

Non-Classical Logics

In the following sections, we shall present some of these logics. The study can be partially based on the notions that were introduced in the previous chapters.

As usual, the presentation will contain motivations, historic landmarks, applications, similarities, and differences with what is already known, and finally indications on how to reason with these logics.

A common feature of these logics is their philosophical origin, which can be explained as a return to the roots: analysis of discourse in natural language, of what is true, what is false, what is neither true nor false, what is necessary, what is contingent, etc.

10.1. Many-valued logics

One of the first conventions that we adopted in the study of logic was to state (in accordance with mathematics) that a reasoning is correct if and only if it is impossible for the premises to be true and the conclusion to be false. But common sense shows that things are not that simple, when we want to begin the analysis before any simplification choice has been made.

Indeed, among the syntactically correct sentences, those we are interested in are declarative sentences and more precisely propositions (i.e. the sets of declarative sentences that are synonyms).

There are declarative sentences that are never assigned truth values, for example,

Honesty is beautiful

whose meaning can only be metaphorical. Others such as

The robot is in the room

can sometimes be true and sometimes be false...

The study of ...