Algebra Seminar talk
2024-11-08
Ivan Chajda
The logic with unsharp implication and negation
Abstract:
Some important logics are based on posets that need not be lattices. An example of such a logic is the logic of quantum mechanics based on am orthomodular poset. It is evident that in this case some logical connectives as disjunction or conjunction may be only partial operations or, as pointed out by us, they may be considered in an "unsharp version", i.e. their result need not be a single element but may be a subset of the poset in question. Hence, also the connective implication is created in this way as "unsharp".