Learning to Classify Logical Formulas Based on Their Semantic Similarity

Abstract

An important task in logic, given a formula and a knowledge base which represents what an agent knows of the current state of the world, is to be able to guess the truth value of the formula. Logic reasoners are designed to perform inferences, that is, to decide whether a formula is a logical consequence of the knowledge base, which is stronger than that and can be intractable in some cases. In addition, under the open-world assumption, it may turn out impossible to infer a formula or its negation. In many practical situations, however, when an agent has to make a decision, it is acceptable to resort to heuristic methods to determine the probable veracity or falsehood of a formula, even in the absence of a guarantee of correctness, to avoid blocking the decisionmaking process and move forward. This is why we propose a method to train a classification model based on available knowledge in order to be able of accurately guessing whether an arbitrary, unseen formula is true or false. Our method exploits a kernel representation of logical formulas based on a model-theoretic measure of semantic similarity. The results of experiments show that the proposed method is highly effective and accurate.

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“…Representing logic formulae as such is an active research domain: for example, in [23], the authors proposed more than a dozen different embedding techniques based on formulae syntax. In communities other than automated deduction, researchers also study first-order formulae representation: for example, in [5], the authors use semantics representation rather than syntax. One can also notice that first-order logic (FOL) is nothing more than a formal language, so abstract syntax trees of FOL are not, in principle, that different from those of programming language statements.…”