Abstract
In traditional propositional logic(PL), the atomic part of formulas are proposition symbols. In first-order logic(FL) the atomic part of formulas are terms, predicates are relations among terms, and quantifiers ∀,∃ are introduced to express the binding of variables ranging over a domain of discourse. We propose a new kind of logics the quantified propositional logic(QL), QL's atomic formulas are in the forms of c, X(p), F(X), where c, p are a propositional symbol, X is a first-order predicate variable and F is a second-order predicate. The quantifiers ∀,∃ are applied on first-order predicate variables. An axiomatic system is given so that the system is sound and complete with the quantified propositional logic. The translations about the quantified propositional logic are given.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have