An introduction to mathematical logic and type theory: to truth through proof
An introduction to mathematical logic and type theory: to truth through proof
Ontological domains, semantic sorts and systematic ambiguity
International Journal of Human-Computer Studies - Special issue: the role of formal ontology in the information technology
Type-logical semantics
Meaning and grammar (2nd ed.): an introduction to semantics
Meaning and grammar (2nd ed.): an introduction to semantics
Categorical Combinators, Sequential Algorithms and Funtional Programming
Categorical Combinators, Sequential Algorithms and Funtional Programming
Meaning and Partiality Revised
SCAI '01 Proceedings of the Seventh Scandinavian Conference on Artificial Intelligence
Anaphora and the Logic of Change
JELIA '90 Proceedings of the European Workshop on Logics in AI
Information states as first class citizens
ACL '92 Proceedings of the 30th annual meeting on Association for Computational Linguistics
Paraconsistent Query Answering Systems
FQAS '02 Proceedings of the 5th International Conference on Flexible Query Answering Systems
Natural language processing using lexical and logical combinators
ICLP'06 Proceedings of the 22nd international conference on Logic Programming
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In order to analyse the semantics of natural language sentences a translation into a partial type logic using lexical and logical combinators is presented. The sentences cover a fragment of English with propositional attitudes like knowledge, belief and assertion. A combinator is a closed term of the lambda calculus possibly containing lexical and/or logical constants. Such combinators seem promising from both a cognitive and computational point of view. There is approximately one lexical combinator for each word, but just eleven logical combinators for the present fragment. The partiality is only used for embedded sentences expressing propositional attitudes, thereby allowing for inconsistency without explosion (also called paraconsistency), and is based on a few key equalities for the connectives giving four truth values (truth, falsehood, and undefinedness with negative and positive polarity; only the first truth value is designated, i.e. yields the logical truths).