Fragmented Reasoning in Natural Language: A Research Program

A common practice in Linguistics today is to analyze the meaning of natural language (NL) using logic. The meaning of a sentence is defined in terms of some truth conditions on a set-theoretical model structure. The translation from sentences to truth conditions is done via an intermediate precise logical language in a compositional way: each syntactic tree of a phrase in the NL is associated with an expression in the logical language (and thereby with a corresponding set-theoretic object in the model), and the meaning expression of a tree is determined by the meaning expressions of its subtrees. This logical characterization is very useful because it provides a mathematically precise description of the meaning of sentences (and their parts). Thus it is possible to see clearly the relation between the meanings of different sentences in terms of equivalence, entailment, contradiction, and so on. Nevertheless, the logical language is usually much more powerful than first-order logic (FOL). Hence, the induced semantic entailment relation is not finitely axiomatizable, and the question whether an arbitrary formula in the logical language is entailed by another is not even semi-decidable. Therefore no computer program could obtain all the valid inferences from a translation of NL text to the logic. But this is not merely a defect of the translation: no computer program could obtain all the valid inferences from a NL text because FOL is a (small) fragment of NL. If we believe in the Church-Turing thesis (that everything that is computable is computable by a Turing machine), then this fact means that also humans are not able to draw all the valid conclusions from NL text. But clearly humans are able to understand NL and draw sufficient inferences from given information in an efficient way. How do they do that? Science is presently far from being able to answer this question. However, one idea that has been suggested as a possible direction for an explanation is that humans do not employ the equivalent of a single massive logical apparatus that takes care of all the inferences, but rather employ many different loosely connected inference modules, each of which specializes on inferences of one kind in a tractable and efficient way. Further “facilitators” combine the results of these modules and transfer information between them. The goal of the research program proposed here is to identify useful types of inferences that are based on NL phenomena. Each inference type provides only a small fragment of the full inference capacity underlying (the translation to logic of) NL, but it is computationally tractable, and (hopefully) complete in some sense (as will be explained below).