148 research outputs found
Multi-dimensional Type Theory: Rules, Categories, and Combinators for Syntax and Semantics
We investigate the possibility of modelling the syntax and semantics of
natural language by constraints, or rules, imposed by the multi-dimensional
type theory Nabla. The only multiplicity we explicitly consider is two, namely
one dimension for the syntax and one dimension for the semantics, but the
general perspective is important. For example, issues of pragmatics could be
handled as additional dimensions.
One of the main problems addressed is the rather complicated repertoire of
operations that exists besides the notion of categories in traditional Montague
grammar. For the syntax we use a categorial grammar along the lines of Lambek.
For the semantics we use so-called lexical and logical combinators inspired by
work in natural logic. Nabla provides a concise interpretation and a sequent
calculus as the basis for implementations.Comment: 20 page
Running a Prover in a Prover - Isabelle as a Meta-Logic
Isabelle provides a foundation of mathematics and I show how you can run your own verified prover directly in the Isabelle prover or as a stand-alone program. I describe the formalization of syntax and semantics and discuss the proof of soundness and completeness for a simple prover for first-order logic
Multi-Agent Programming Contest 2011 - The Python-DTU Team
We provide a brief description of the Python-DTU system, including the
overall design, the tools and the algorithms that we plan to use in the agent
contest.Comment: 4 page
NaDeA: A Natural Deduction Assistant with a Formalization in Isabelle
We present a new software tool for teaching logic based on natural deduction.
Its proof system is formalized in the proof assistant Isabelle such that its
definition is very precise. Soundness of the formalization has been proved in
Isabelle. The tool is open source software developed in TypeScript / JavaScript
and can thus be used directly in a browser without any further installation.
Although developed for undergraduate computer science students who are used to
study and program concrete computer code in a programming language we consider
the approach relevant for a broader audience and for other proof systems as
well.Comment: Proceedings of the Fourth International Conference on Tools for
Teaching Logic (TTL2015), Rennes, France, June 9-12, 2015. Editors: M.
Antonia Huertas, Jo\~ao Marcos, Mar\'ia Manzano, Sophie Pinchinat,
Fran\c{c}ois Schwarzentrube
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