Non-classical logic: The basics
Prerequisite: Foundations of Logic
In Foundations of Logic you learn, first, that every proposition is either true or false and, second, that some propositions are tautologies, i.e., true under every assignment, and can thus be turned into corresponding inference rules that allow you to derive a formula from other formulas (or the empty set). Among these are, e.g.,
Modus Ponens: p, p --> q // q
Double Negation: ~~p // p
Excluded Middle: // p v ~p
De Morgan: p v ~p // ~(p & ~p)
While all this is intuitively plausible (and quite useful), none of it HAS TO BE THAT WAY.
There is no reason, in principle, why there should be only two truth values, true and false. Why not three, four, five, or infinitely many? And there is no reason, in principle, why every proposition should have one and only one truth value. Why can't there be 'truth value gaps', i.e., propositions which have no truth value at all? Or 'truth value gluts', i.e., propositions which have more than one truth value?
Depending on what changes you make to classical logic, you end up with different logical systems that are NON-CLASSICAL.
In paraconsistent logic, for instance, p & ~p is not necessarily false - there can be true contradictions.
In intuitionist logic, for instance, ~~p iff p and p v ~p are not necessarily true.
And so on and so forth.
The lecture first recaps classical logic and then provides an introduction into the foundations of non-classical logics, in particular non-truth-functional modal logic, conditional logic, intuitionist logic, paraconsistent logic, many-valued logic(s) and relevance logic.
Veranstaltungsart: Vorlesung (Offizielle Lehrveranstaltungen)
Zeiten: Do. 08:00 - 10:00 (wöchentlich)
Erster Termin: Donnerstag, 13.04.2023 08:00 - 10:00, Ort: 93/E31
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- Cognitive Science > Master-Programm