Unification in Pretabular Extensions of S4

E-Unification for Subsystems of S4

This paper is concerned with the uniication problem in the path logics associated by the optimised functional translation method with the propositional modal logics K, KD, KT, KD4, S4 and S5. It presents improved uniication algorithms for certain forms of the right identity and associativity laws. The algorithms employ mutation rules, which have the advantage that terms are worked oo from the o...

Topological completeness of extensions of S4

Perhaps the most celebrated topological completeness result in modal logic is the McKinseyTarski theorem that if we interpret modal diamond as topological closure, then S4 is complete for the real line or indeed any dense-in-itself separable metrizable space [10]. This result was proved before relational semantics for modal logic was introduced. In the last 15 years, utilizing relational semant...

Lattices of Modal Logics and Their Groups of Automorphisms

The present paper investigates the groups of automorphisms for some lattices of modal logics. The main results are the following. The lattice of normal extensions of S4.3, NExtS4.3, has exactly two automorphisms, NExtK.alt1 has continuously many automorphisms. Moreover, any automorphism of NExtS4 fixes all logics of finite codimension. We also obtain the following characterization of pretabular...

Unitary Unification of S 5 Modal Logic and Its Extensions

It is shown that all extensions of S5 modal logic, both in the standard formalization and in the formalization with strict implication, as well as all varieties of monadic algebras have unitary unification.

A Survey of Linguistically Motivated Extensions to Unification-Based Formalisms