The aim of this article is to strengthen links between cognitive brain research and formal logic. The work covers three fundamental sorts of logical inferences: reasoning in the propositional calculus, i.e. inferences with the conditional ‘‘if...then’’, reasoning in the predicate calculus, i.e. inferences based on quantifiers such as ‘‘all’’, ‘‘some’’, ‘‘none’’, and reasoning with n-place relat...

If A is logically equivalent to B, it is not necessary that #(A) = p(B). This technical note proves, however, that if A is in CNF, there exists some logically equivalent DNF, B, such that p(A) = #(B). It is well known that this admits anomalies, such as #(P/x ~P) > 0 and #(P v ~P) < 1. Further, two logically equivalent expressions can have different possibility values. For example, P v Q-~(P ^ ...

Knowledge bases theory provide an important example of the field where applications of universal algebra and algebraic logic look very natural, and their interaction with practical problems arising in computer science might be very productive. In this paper we study the equivalence problem for knowledge bases. Our interest is to find out how the informational equivalence is related to the logic...