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...

In this paper, we propose a set theoretic approach for knowledge representation. While the syntax of an application domain is captured by set theoretic constructs including individuals, concepts and operators, knowledge is formalized by equality assertions. We first present a primitive form that uses minimal assumed knowledge and constructs. Then, assuming naive set theory, we extend it by defi...

Dependence logic is a new logic which incorporates the notion of “dependence”, as well as “independence” between variables into first-order logic. In this thesis, we study extensions and variants of dependence logic on the first-order, propositional and modal level. In particular, the role of intuitionistic connectives in this setting is emphasized. We obtain, among others, the following result...

The logic of equality with uninterpreted functions (EUF) and its extensions have been widely applied to processor verification, by means of a large variety of progressively more sophisticated (lazy or eager) translations into propositional SAT. Here we propose a new approach, namely a general DPLL(X) engine, whose parameter X can be instantiated with a specialized solver Solver T for a given th...

We investigate the system TRC of untyped illative combinatory logic that is equiconsistent with New Foundations. We prove that various unstratified combinators do not exist in TRC. Introduction. We prove some results in the axiomatic system TRC introduced in [3]. The system TRC (for ‘type-respecting combinators’) is an untyped system of combinatory logic, in the sense of [1], [2]. TRC is a firs...