Higher order logic

On the compactness property of extensions of first-order G"{o}del logic

We study three kinds of compactness in some variants of G"{o}del logic: compactness,entailment compactness, and approximate entailment compactness.For countable first-order underlying language we use the Henkinconstruction to prove the compactness property of extensions offirst-order g logic enriched by nullary connective or the Baaz'sprojection connective. In the case of uncountable first-orde...

Higher-order Logic Programming Higher-order Logic Programming Y Contents 1 Introduction 3 2 Motivating a Higher-order Extension to Horn Clauses 5 3 a Higher-order Logic 12

Embedding of Quantified Higher-Order Nominal Modal Logic into Classical Higher-Order Logic

In this paper, we present an embedding of higher-order nominal modal logic into classical higher-order logic and study its automation. There exists no automated theorem prover for first-order or higherorder nominal logic at the moment, hence, this is the first automation for this kind of logic. In our work, we focus on nominal tense logic and have successfully proven some first theorems.

SOUND AND COMPLETE TRANSLATIONSFROM SORTED HIGHER - ORDER LOGICINTO SORTED FIRST - ORDER LOGICManfred

Extending existing calculi by sorts is a strong means for improving the deductive power of rst-order theorem provers. Since many mathematical facts can be more easily expressed in higher-order logic { aside the greater power of higher-order logic in principle {, it is desirable to transfer the advantages of sorts in the rst-order case to the higher-order case. One possible method for automating...

Minimum Model Semantics for Extensional Higher-order Logic Programming with Negation

Extensional higher-order logic programming has been introduced as a generalization of classical logic programming. An important characteristic of this paradigm is that it preserves all the well-known properties of traditional logic programming. In this paper we consider the semantics of negation in the context of the new paradigm. Using some recent results from non-monotonic fixed-point theory,...

A Call-by-Need Strategy for Higher-Order Functional-Logic Programming

We present an approach to truely higher order functional logic programming based on higher order narrowing Roughly speaking we model a higher order functional core language by higher order rewriting and extend it by logic variables For the integration of logic programs conditional rules are supported For solving goals in this framework we present a complete calcu lus for higher order conditiona...