Type theoretic semantics for SemNet
Semantic Networks have long been recognised as an important tool for modelling human type reasoning. This paper describes an attempt to give a formal semantics of a semantic network in constructive type theory.
The particular net studied is SemNet, the internal knowledge representation for LOLITA: a large scale natural language engineering system. SemNet has been designed with large scale, efficiency, integration and expressiveness in mind. It supports many different forms of plausible and valid reasoning, including: analogy, epistemic reasoning and inheritance. Type theory is used to define the syntactic and semantic models of SemNet. Because of the notion of an internal logic, which follows from the ‘propositions as types’ principle, both of these models can be reasoned about in the same framework. Once formal semantics have been defined they can then be used to analyse the different reasoning mechanisms.
A further advantage is that (because of applications to formal methods for software engineering) type checkers/proof assistants have been built. These tools are ideal for organising and managing the analysis of formal models.
The models are shown to be useful in analysing correctness of implementation of the algorithms, proving consistency and highlighting the assumptions and meaning of the valid and plausible reasoning.
KeywordsType Theory Semantic Network Formal Semantic Reasoning Mechanism Proof Assistant
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