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A COMPUTATIONAL SEMANTICS FOR IMPLICATIVES
Cleo Condoravdi and Lauri Karttunen Sponsored by the Stanford Humanities Center/Mellon Foundation Graduate Research Program In a 1971 article titled ``The Logic of English Predicate Complement Constructions'' Lauri Karttunen wrote
It is evident that logical relations between main sentences and
their complements are of great significance in any system of
automatic data processing that depends on natural language. For
this reason, the systematic study of such relations, of which this
paper is an example, will certainly have a great practical value,
in addition to what it may contribute to the theory of the
semantics of natural languages.
It is only now that this 35-year old prediction is becoming a reality in the broader context of automated question answering and reasoning. Recognizing whether a given piece of text can be inferred from another piece of text is, arguably, a minimal criterion for Natural Language Understanding and the semantics of complement constructions is an important part of that task. A system that computes textual inferences should be able to deduce, for example, that (1b) and (1c) follow from (1a). (1) a. Ed forgot to close the door.
b. Ed intended to close the door. c. Ed did not close the door. In this paper we present a computational semantics for the entailments of implicative constructions. Central to this is an implication projection algorithm calculating the implications of a sentence with an arbitrary number of embedding of implicative and factive predicates. We can thus automatically conclude that ``The diplomat does not know that the president didn't forget to force the general to resign last week'' implies that the general resigned last week, while ``The diplomat knows that the president didn't manage to make the general resign'' implies that the general did not resign. These implication patterns depend on the embedding predicates and the polarity of the environment in which they occur. Polarity is a relative notion. The polarity of any given level of structure depends on the sequence of potential polarity switches stretching back to the matrix clause. A verb in a negative clause does not necessarily give raise to a negative environment since the negativity of ``not'' may be neutralized by another negative as in example (2). (2) Ed refused not to attempt to escape.
Given a pair of sentences, a matrix sentence and a complement clause, the system attempts to determine whether the complement (or its negation) follows from the sentence as a whole. Entailment and contradiction detection is performed by a process of matching, a lightweight inference mechanism that operates on flat representations that are partitioned into contexts. The content of the top level context represents what the author of the sentence is taken to be committed to. Negation and intentional operators trigger the introduction of new contexts. This is the first systematic implementation of textual inferences arising from the different types of implicative verbs and their interaction with factive verbs. The implementation is part of an end-to-end system with English sentences as input and a system answer indicating the logical relation between two sentences, distinguishing between entailment, contradiction and compatibility. 
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