Exact Unification and Admissibility

From Admissibility to a New Hierarchy of Unification Types

Motivated by the study of admissible rules, a new hierarchy of “exact” unification types is introduced where a unifier is more general than another unifier if all identities unified by the first are unified by the second. A Ghilardi-style algebraic interpretation of this hierarchy is presented that features exact algebras rather than projective algebras. Examples of equational classes distingui...

Rules with parameters in modal logic I

We study admissibility of inference rules and unification with parameters in transitive modal logics (extensions of K4), in particular we generalize various results on parameterfree admissibility and unification to the setting with parameters. Specifically, we give a characterization of projective formulas generalizing Ghilardi’s characterization in the parameter-free case, leading to new proof...

Unification in the normal modal logic Alt1

The unification problem in a logical system L can be defined in the following way: given a formula φ(x1, . . . , xα), determine whether there exists formulas ψ1, . . ., ψα such that φ(ψ1, . . . , ψα) is in L. The research on unification for modal logics was originally motivated by the admissibility problem for rules of inference: given a rule of inference φ1(x1, . . . , xα), . . . , φm(x1, . . ...

Multi-modal and Temporal Logics with Universal Formula - Reduction of Admissibility to Validity and Unification

The article studies multi-modal (in particular temporal, tense, logics) possessing universal formulas. We prove (Theorems 11 and 12) that the admissibility problem for inference rules (inference rules with parameters) is decidable for all decidable multi-modal (in particular, temporal) logics possessing an universal formula and decidable w.r.t. unification (unification with parameters). These t...

Admissibility and Unifiability in Contact Logics