The Completeness of Carnap's Predicate Logic

On the scope of the completeness theorem for first-order predicate logic∗

The problem of completeness of classical first-order predicate logic was formulated, for the first time in precise mathematical terms, in 1928 by Hilbert and Ackermann in [16] and solved positively by Gödel in his Ph.D. thesis one year later [8, 9]. In 1947 Henkin [14, 15] presented an alternative simpler proof that has become standard in logic textbooks. The main advantage of Henkin’s proof is...

On completeness results for predicate

In this paper we deal with generic expansions of first-order predicate logics of some left-continuous t-norms with a countable set of truth-constants. Besides already known results for the case of Lukasiewicz logic, we obtain new conservativeness and completenesss results for some other expansions. Namely, we prove that the expansions of predicate Product, Gödel and Nilpotent Minimum logics wit...

Predicate logic

Predicate logic is a sub-discipline of logic that had its roots in the last quarter of the nineteenth century, though it had to wait until the second decade of the twentieth century for a solid foundation. Like any other logic, it is concerned with the validity of arguments, though not of any kind: its interest lies in reasoning about what is universally true. As such, predicate logic is especi...

Completeness of two systems of illative combinatory logic for first-order propositional and predicate calculus

Illative combinatory logic consists of the theory of combinators or lambda calculus extended by extra constants (and corresponding axioms and rules) intended to capture inference. The paper considers 4 systems of illative combinatory logic that are sound for first-order propositional and predicate calculus.

The Predicate-Minimizing Logic MIN