429 research outputs found
Bootstrapping Lexical Choice via Multiple-Sequence Alignment
An important component of any generation system is the mapping dictionary, a
lexicon of elementary semantic expressions and corresponding natural language
realizations. Typically, labor-intensive knowledge-based methods are used to
construct the dictionary. We instead propose to acquire it automatically via a
novel multiple-pass algorithm employing multiple-sequence alignment, a
technique commonly used in bioinformatics. Crucially, our method leverages
latent information contained in multi-parallel corpora -- datasets that supply
several verbalizations of the corresponding semantics rather than just one.
We used our techniques to generate natural language versions of
computer-generated mathematical proofs, with good results on both a
per-component and overall-output basis. For example, in evaluations involving a
dozen human judges, our system produced output whose readability and
faithfulness to the semantic input rivaled that of a traditional generation
system.Comment: 8 pages; to appear in the proceedings of EMNLP-200
Virtual Evidence: A Constructive Semantics for Classical Logics
This article presents a computational semantics for classical logic using
constructive type theory. Such semantics seems impossible because classical
logic allows the Law of Excluded Middle (LEM), not accepted in constructive
logic since it does not have computational meaning. However, the apparently
oracular powers expressed in the LEM, that for any proposition P either it or
its negation, not P, is true can also be explained in terms of constructive
evidence that does not refer to "oracles for truth." Types with virtual
evidence and the constructive impossibility of negative evidence provide
sufficient semantic grounds for classical truth and have a simple computational
meaning. This idea is formalized using refinement types, a concept of
constructive type theory used since 1984 and explained here. A new axiom
creating virtual evidence fully retains the constructive meaning of the logical
operators in classical contexts.
Key Words: classical logic, constructive logic, intuitionistic logic,
propositions-as-types, constructive type theory, refinement types, double
negation translation, computational content, virtual evidenc
A User-Level Introduction to the Nuprl Proof Development System
This document is intended to introduce the key elements of the Nuprl Proof Development System (Nuprl, for short) from the perspective of a Nuprl user, as opposed to the perspective of someone intimately involved in developing or extending Nuprl. As such, it may be more appropriate than other Kuprl-related documents for readers who are primarily concerned with uses of Nuprl and not fine details of Nuprl\u27s mathematical foundation. It introduces and illustrates key Kuprl concepts -such as types, terms, displayforms, and tactics - in the framework of a model of calculational predicate logic inference
A Framework for Program Development Based on Schematic Proof
Often, calculi for manipulating and reasoning about programs can be recast as calculi for synthesizing programs. The difference involves often only a slight shift of perspective: admitting metavariables into proofs. We propose that such calculi should be implemented in logical frameworks that support this kind of proof construction and that such an implementation can unify program verification and synthesis. Our proposal is illustrated with a worked example developed in Paulson's Isabelle system. We also give examples of existent calculi that are closely related to the methodology we are proposing and others that can be profitably recast using our approach
A Computational Approach to Reflective Meta-Reasoning about Languages with Bindings
We present a foundation for a computational meta-theory of languages with bindings implemented in a computer-aided formal reasoning environment. Our theory provides the ability to reason abstractly about operators, languages, open-ended languages, classes of languages, etc. The theory is based on the ideas of higher-order abstract syntax, with an appropriate induction principle parameterized over the language (i.e. a set of operators) being used. In our approach, both the bound and free variables are treated uniformly and this uniform treatment extends naturally to variable-length bindings. The implementation is reflective, namely there is a natural mapping between the meta-language of the theorem-prover and the object language of our theory. The object language substitution operation is mapped to the meta-language substitution and does not need to be defined recursively. Our approach does not require designing a custom type theory; in this paper we describe the implementation of this foundational theory within a general-purpose type theory. This work is fully implemented in the MetaPRL theorem prover, using the pre-existing NuPRL-like Martin-Lof-style computational type theory. Based on this implementation, we lay out an outline for a framework for programming language experimentation and exploration as well as a general reflective reasoning framework. This paper also includes a short survey of the existing approaches to syntactic reflection
Computer theorem proving in math
We give an overview of issues surrounding computer-verified theorem proving
in the standard pure-mathematical context. This is based on my talk at the PQR
conference (Brussels, June 2003)
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