Computational Issues in Calculi of Partial Inductive Definitions
We study the properties of a number of algorithms proposed to explore the computational space generated by a very simple and general idea: the notion of a mathematical definition and a number of suggested formal interpretations ofthis idea. Theories of partial inductive definitions (PID) constitute...
Main Author: | |
---|---|
Format: | Doctoral Thesis |
Language: | English |
Published: |
Decisions, Networks and Analytics lab
1995
|
Subjects: | |
Online Access: | http://urn.kb.se/resolve?urn=urn:nbn:se:ri:diva-21196 |
id |
ndltd-UPSALLA1-oai-DiVA.org-ri-21196 |
---|---|
record_format |
oai_dc |
spelling |
ndltd-UPSALLA1-oai-DiVA.org-ri-211962017-10-13T05:15:52ZComputational Issues in Calculi of Partial Inductive DefinitionsengKreuger, PerDecisions, Networks and Analytics lab1995Theory of computationalgorithmslogicproof-theorypartial inductive defi-nitionsdefinitional reflectiondisunificationclosurecompletionnegationconstructive negationquantificationlogic programmingmeta programmingquantificationskolemizationself-referenceprogram semanticsdeclarative controlproof-searchtheorem-proving.Computer and Information ScienceData- och informationsvetenskapWe study the properties of a number of algorithms proposed to explore the computational space generated by a very simple and general idea: the notion of a mathematical definition and a number of suggested formal interpretations ofthis idea. Theories of partial inductive definitions (PID) constitute a class of logics based on the notion of an inductive definition. Formal systems based on this notion can be used to generalize Horn-logic and naturally allow and suggest extensions which differ in interesting ways from generalizations based on first order predicate calculus. E.g. the notion of completion generated by a calculus of PID and the resulting notion of negation is completely natural and does not require externally motivated procedures such as "negation as failure". For this reason, computational issues arising in these calculi deserve closer inspection. This work discuss a number of finitary theories of PID and analyzethe algorithmic and semantical issues that arise in each of them. There has been significant work on implementing logic programming languages in this setting and we briefly present the programming language and knowledge modelling tool GCLA II in which many of the computational prob-lems discussed arise naturally in practice. <p>Also published as SICS Dissertation no. SICS-D-19</p>Doctoral thesis, monographinfo:eu-repo/semantics/doctoralThesistexthttp://urn.kb.se/resolve?urn=urn:nbn:se:ri:diva-21196SICS dissertation series, 1101-1335 ; SICS-D-19application/postscriptinfo:eu-repo/semantics/openAccess |
collection |
NDLTD |
language |
English |
format |
Doctoral Thesis |
sources |
NDLTD |
topic |
Theory of computation algorithms logic proof-theory partial inductive defi-nitions definitional reflection disunification closure completion negation constructive negation quantification logic programming meta programming quantification skolemization self-reference program semantics declarative control proof-search theorem-proving. Computer and Information Science Data- och informationsvetenskap |
spellingShingle |
Theory of computation algorithms logic proof-theory partial inductive defi-nitions definitional reflection disunification closure completion negation constructive negation quantification logic programming meta programming quantification skolemization self-reference program semantics declarative control proof-search theorem-proving. Computer and Information Science Data- och informationsvetenskap Kreuger, Per Computational Issues in Calculi of Partial Inductive Definitions |
description |
We study the properties of a number of algorithms proposed to explore the computational space generated by a very simple and general idea: the notion of a mathematical definition and a number of suggested formal interpretations ofthis idea. Theories of partial inductive definitions (PID) constitute a class of logics based on the notion of an inductive definition. Formal systems based on this notion can be used to generalize Horn-logic and naturally allow and suggest extensions which differ in interesting ways from generalizations based on first order predicate calculus. E.g. the notion of completion generated by a calculus of PID and the resulting notion of negation is completely natural and does not require externally motivated procedures such as "negation as failure". For this reason, computational issues arising in these calculi deserve closer inspection. This work discuss a number of finitary theories of PID and analyzethe algorithmic and semantical issues that arise in each of them. There has been significant work on implementing logic programming languages in this setting and we briefly present the programming language and knowledge modelling tool GCLA II in which many of the computational prob-lems discussed arise naturally in practice. === <p>Also published as SICS Dissertation no. SICS-D-19</p> |
author |
Kreuger, Per |
author_facet |
Kreuger, Per |
author_sort |
Kreuger, Per |
title |
Computational Issues in Calculi of Partial Inductive Definitions |
title_short |
Computational Issues in Calculi of Partial Inductive Definitions |
title_full |
Computational Issues in Calculi of Partial Inductive Definitions |
title_fullStr |
Computational Issues in Calculi of Partial Inductive Definitions |
title_full_unstemmed |
Computational Issues in Calculi of Partial Inductive Definitions |
title_sort |
computational issues in calculi of partial inductive definitions |
publisher |
Decisions, Networks and Analytics lab |
publishDate |
1995 |
url |
http://urn.kb.se/resolve?urn=urn:nbn:se:ri:diva-21196 |
work_keys_str_mv |
AT kreugerper computationalissuesincalculiofpartialinductivedefinitions |
_version_ |
1718553568794902528 |