The Boolean algebra of formulas of first-order logic

Parsing permutations of first-order propositional logic formulas

In this work, we wish to determine the complexity of deciding whether a given multiset of symbols, chosen from some finite set of symbols, can be derived according to the rules of a given context-free grammar. Providing an upper bound for this problem is of interest to computational linguistics, one goal of which is to classify the complexity of parsing and understanding natural language. We co...

Logic Programs vs. First-Order Formulas in Textual Inference

In the problem of recognizing textual entailment, the goal is to decide, given a text and a hypothesis expressed in a natural language, whether a human reasoner would call the hypothesis a consequence of the text. One approach to this problem is to use a first-order reasoning tool to check whether the hypothesis can be derived from the text conjoined with relevant background knowledge, after ex...

First-Order Loop Formulas for Normal Logic Programs

In this paper we extend Lin and Zhao’s notions of loops and loop formulas to normal logic programs that may contain variables. Under our definition, a loop formula of such a logic program is a first-order sentence. We show that together with Clark’s completion, our notion of first-order loop formulas captures the answer set semantics on the instantiationbasis: for any finite set F of ground fac...

Deciding CLU Logic Formulas via Boolean and Pseudo-Boolean Encodings

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...