8742017
Two Extensions of PX system
Abstract Two extensions of PX system will be discussed. The extensions are ctPX (catch/throw PX) and mvPX (multiple values PX). ctPX is a PX system extended with Nakano's catch/throw logic. ctPX enables to extract LISP programs with catch/throw mechanism form natural proofs. mvPX is a PX system which uses multiple values rather than lists to keep a finite sequences of data. Programs extracted by ctPX are more efficient than the ones by the original PX.
28922785
Realizability Interpretation of Generalized Inductive Definitions
Generalized inductive definitions give a way of defining a predicate as the least solution P of the equation [email protected]?A[P] where a predicate variable P may occur in a formula A[P] positively. This paper gives aq-realizability interpretation of generalized inductive definitions and proves the soundness of the interpretation.
38971633
A New Translation for Semi-classical Theories - Backtracking without CPS
Most research of algorithm extraction from classical proofs is based on double negation translation or its variants. From the viewpoint of Curry-Howard isomorphism, double negation translation corresponds to CPS translation. Unfortunately, CPS translation makes resulting programs very complex. 
 
In this paper, we study a new translation for a semi-classical logic which is not based on double negation translation. Though it does not validate full classical logic, it translates Limit Computable Mathematics (LCM) into constructive mathematics. 
 
Our translation is inspired by game semantics with backtracking rules. Using the translation, we can extract an algorithm from a proof of a proposition A in LCM. The extracted algorithm gives a recursive winning strategy for the first mover of the game defined from A, at least when A is implication-free.
11284896
Semantic Wiki as a Lightweight Knowledge Management System
Since its birth in 1995, Wiki has become more and more popular This paper presents a Semantic Wiki, a Wiki extended to include the ideas of Semantic Web The proposed Semantic Wiki uses a simple Wiki syntax to write labeled links which represent RDF triples By enabling the writing of labeled links, Semantic Wiki may provide an easy-to-use and flexible environment for an integrated management of content and metadata, so that Semantic Wiki may be used as a lightweight knowledge management system.
30034887
Horn Clause Computation with DNA Molecules
In this paper, we will propose Horn clause computation as an underlying computational framework of DNA computer. Horn clause program is a subclass of the formulas of first order logic and has close relation to PROLOG language. The computational power of Horn clauses was discussed in (Tärnland, 1977) and it was shown that a finite set of Horn clauses is computationally equivalent to Turing Machine. Furthermore, it should be noted that Horn programs are adequate for representing nondeterministic computation. Thus, its parallel implementation with huge number of molecules might have possibility to overcome the computational power of conventional computers. It should also be noted that the clear logical semantics of Horn programs might enable us to accept it as a higher-level programming language of DNA computer. The aim of this paper is to propose an experimental method for implementing deduction with a subclass of Horn programs, called simple Horn programs. The computational power of this model is theoretically investigated and demonstrated with some applications to NP-complete problems.
62399989
Proceedings of the 8th international conference on Grammatical Inference: algorithms and applications