SCL(EQ): SCL for First-Order Logic with Equality

Equality and Monodic First-Order Temporal Logic

It has been shown recently that monodic first-order temporal logic without functional symbols but with equality is incomplete, i.e. the set of the valid formulae of this logic is not recursively enumerable. In this paper we show that an even simpler fragment consisting of monodic monadic two-variable formulae is not recursively enumerable.

Reflecting Proofs in First-Order Logic with Equality

Our general goal is to provide better automation in interactive proof assistants such as Coq. We present an interpreter of proof traces in first-order multi-sorted logic with equality. Thanks to the reflection ability of Coq, this interpreter is both implemented and formally proved sound — with respect to a reflective interpretation of formulae as Coq properties — inside Coq’s type theory. Our ...

Guarded Fragment Of First Order Logic Without Equality

Let n be nite. Let Ln denotes the n-variable rst order logic without equality, whose semantics are provided by generalized models, where assignments are allowed from arbitrary sets of n-ary sequences V ⊆ nU (some non empty set U). Semantics for the Boolean connectives are de ned the usual way, and for the existential quanti er ∃xi (i < n), a generalized model V and s ∈ V , V, s |= ∃xiφ⇐⇒ (∃s)(s...

Some New Strategies for Theorem-Proving in First Order Logic with Equality

A method for encoding formulas in rst-order logic with equality into some equational logics and their associated propositional logics is presented. This yields some new strategies for theorem-proving in rst-order logic with equality. We outline the techniques and give a simple illustration of their use.

First Order Logic with Dependent