# Semantic representations and interpretation

Formal semantics of natural languages has its roots in logic. It consists in – on the one hand – constructing well defined logical languages reflecting logical semantic aspects of the natural language. That they are well-defined means that they not only have a well-defined syntax, but also a consequence relation either defined through semantics and logical validity or through an inference calculus. On the other hand, formal semantics specify rules for mapping linguistic structure onto these representations.

In natural language processing, there have been developed several formalisms and large grammars where one goal is to map sentences to some sort of semantic representations. One example is the English Resource Grammar, which maps sentences to representations in what is called Minimal Recursion Semantics (MRS). The representation language of MRS is based on first-order logic. One goal has been to underspecify scope relations compared to first-order logic such that one MRS structure represents several formulas. But MRS representations also contain constructions which cannot be directly interpreted as first-order logical formulas. Examples include coordination structures, sentences as arguments of predicates, and events unbound by quantifiers.

Another fom of semantic representation langauge is Abstract Meaning Representation (AMR) which has become more popular in the recent years. AMR uses a class of graphs to represent sentence content. The graphs carry a structure more similar to syntactic structure than traditional logical form, but leaves some open questions regarding their interpretation.

The goal of this project is to consider these formalisms and their possible interpretations in terms of logic

Suitable background: Some knowledge of (or willingness to learn) logic and computational semantics.