A note about connection of the first-order functional calculus with many-valued propositional calculi.

Approximating Propositional Calculi by Finite-Valued Logics

Bernays introduced a method for proving underivability results in propositional calculi C by truth tables. It is investigated how far this method can be carried using (1) one or (2) an infinite sequence of many-valued logics. It is shown that the best candidate matrices for (1) can be computed from the calculus, and how sequences for (2) can be found for certain classes of logics. Furthermore, ...

A First-Order Calculus Based on Propositional BDDs

Many-Valued First-Order Logics with Probabilistic Semantics

We present n-valued rst-order logics with a purely proba-bilistic semantics. We then introduce a new probabilistic semantics of n-valued rst-order logics that lies between the purely probabilistic semantics and the truth-functional semantics of the n-valued Lukasiewicz logics Ln. Within this semantics, closed formulas of classical rst-order logics that are logically equivalent in the classical ...

Implementing Connection Calculi for First-order Modal Logics

This paper presents an implementation of an automated theorem prover for first-order modal logic that works for the constant, cumulative, and varying domain of the modal logics D, T, S4, and S5. It is based on the connection calculus for classical logic and uses prefixes representing world paths and a prefix unification algorithm to capture the restrictions given by the Kripke semantics of the ...

Proof Search for the First-Order Connection Calculus in Maude

This paper develops a rewriting logic specification of the connection method for first-order logic, implemented in Maude. The connection method is a goal-directed proof procedure that requires a careful control over clause copies. The specification separates the inference rule layer from the rule application layer, and implements the latter at Maude’s meta-level. This allows us to develop and c...