Kripke Completeness of Infinitary Predicate Multimodal Logics

On Kripke completeness of some modal predicate logics

Let us recall some basic definitions and notation; most of them are the same as in the book [3]. Atomic formulas are constructed from predicate letters P k (countably many for each arity n ≥ 0) and a countable set of individual variables V ar, without constants and function letters. Modal (predicate) formulas are obtained from atomic formulas by applying classical propositional connectives, qua...

Kripke Completeness for Intermediate Logics

Non-Monotonic Predicate Logics Syntax, Semantics, Completeness

To simplify our account, rewrite your favorite usual predicate logic, classical, modal, intuitionistic, as a logic of the set L of all statements. This is an inessential change. As Tarski once did, arrange it so that only statements occur in all axioms a and rules of inference I, all of which have the (monotonic) form ”from a, a, ..., infer a. Then a deductively closed set D is merely a subset ...

Kripke Completeness of First-Order Constructive Logics with Strong Negation

This paper considers Kripke completeness of Nelson’s constructive predicate logic N3 and its several variants. N3 is an extension of intuitionistic predicate logic Int by an contructive negation operator ∼ called strong negation. The variants of N3 in consideration are by omitting the axiom A → (∼A → B), by adding the axiom of constant domain ∀x(A(x) ∨ B) → ∀xA(x) ∨ B, by adding (A → B) ∨ (B → ...

A General Proof of Kripke-completeness for Quantified Modal Logics