In this paper, we present a novel rst order theorem proving strategy { ordered semantic hyper linking. Ordered semantic hyper linking (OSHL) is an instance-based refutational theorem proving strategy. It is sound and complete. OSHL has an eecient propositional decision procedure. It solves rst order problems by reducing them to propositional problems. It uses natural semantics of an input probl...

We analyse the role of the modal axiom corresponding to the first-order formula “∃y (x = y)” in axiomatisations of two-dimensional propositional modal logics. One of the several possible connections between propositional multi-modal logics and classical first-order logic is to consider finite variable fragments of the latter as ‘multi-dimensional’ modal formalisms: First-order variable-assignme...

A framework is developed that extends calculi for propositional, modal and predicate logics to calculi for team-based logics. This method is applied to classical and quantified propositional logic, first-order logic and the modal logic K. Complete axiomatizations for propositional team logic PTL, quantified propositional team logic QPTL, modal team logic MTL and the dependence-atom-free fragmen...

MTL-algebras are algebraic structures for the Esteva-Godo monoidal tnorm based logic (MTL), a many-valued propositional calculus that formalizes the structure of the real interval [0, 1], induced by a left-continuous t-norm. Given a complete MTL-algebra X , we define the weak forcing value |φ|X and the forcing value [φ]X , for any formula φ of MTL in X . We establish some arithmetical propertie...

Polytypic functions have mainly been studied in the context of functional programming languages. In that setting, applications of polytypism include elegant treatments of polymorphic equality, prettyprinting, and the encoding and decoding of high-level datatypes to and from low-level binary formats. In this paper, we discuss how polytypism supports some aspects of theorem proving: automated ter...