Probabilistic Type Theory and Natural Language Semantics

Linguistic Issues in Language Technology – LiLT Submitted, November 2015 Probabilistic Type Theory and Natural Language Semantics Robin Cooper1, Simon Dobnik1, Shalom Lappin1,2, and Staffan Larsson1, 1University of Gothenburg, 2King’s College London Published by CSLI Publications LiLT volume 10, issue (4) November 2015 Probabilistic Type Theory and Natural Language Semantics Robin Cooper1, Simon Dobnik1, Shalom Lappin1,2, and Staffan Larsson1, 1University of Gothenburg, 2King’s College London Abstract Type theory has played an important role in specifying the formal con- nection between syntactic structure and semantic interpretation within the history of formal semantics. In recent years rich type theories de- veloped for the semantics of programming languages have become in- fluential in the semantics of natural language. The use of probabilistic reasoning to model human learning and cognition has become an in- creasingly important part of cognitive science. In this paper we offer a probabilistic formulation of a rich type theory, Type Theory with Records (TTR), and we illustrate how this framework can be used to approach the problem of semantic learning. Our probabilistic version of TTR is intended to provide an interface between the cognitive process of classifying situations according to the types that they instantiate, and the compositional semantics of natural language. 1 LiLT Volume 10, Issue (4), November 2015. Probabilistic Type Theory and Natural Language Semantics. Copyright c ⃝ 2015, CSLI Publications. 2 / LiLT volume 10, issue (4) November 2015 1 Probabilistic Semantics In a classical semantic theory meaning is defined in terms of truth con- ditions. The meaning of a sentence is built up compositionally through a sequence of functions from the semantic values of constituent ex- pressions to the value of the expression formed from these syntactic elements (Montague, 1974). Underspecified semantic theories weaken the connection between the meaning of a phrase and its constituents from a function to a relation (see Fox and Lappin, 2010 for discus- sion and references). Dynamic semantic accounts incorporate update procedures for incrementally computing the effect of new information on the interpretation of sentences in discourse and dialogue (see, for example, Kamp and Reyle, 1993). In all of these frameworks the type system is categorical. A type T identifies a set of possible denotations for expressions in T, and the system specifies combinatorial operations for deriving the denotation of an expression from the values of its con- stituents. There are at least two problems with these frameworks. First, they cannot represent the gradience of semantic properties that is pervasive in speakers’ judgements concerning truth, predication, and meaning relations. In general, predicates do not have determinate extensions (or intensions), and so, in many cases, speakers do not make categor- ical judgements about the interpretation of an expression. One might seek to attribute such gradience effects to performance factors, such as memory limitations and attentional focus, on the realization of seman- tic competence. Unless one can provide a precise explanation of per- formance mechanisms and how they produce the observed gradience phenomena, then such an account will have little if any explanatory …

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