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Extensional Higher-Order Logic Programming

2013
*
ACM Transactions on Computational Logic
*

We propose a purely

doi:10.1145/2499937.2499942
fatcat:ek66hrnijjawbofxnnnq4ymksq
*extensional*semantics for*higher*-*order**logic**programming*. ... In other words, we provide a purely*extensional*theoretical framework for*higher*-*order**logic**programming*which generalizes the familiar theory of classical (first-*order*)*logic**programming*. ... There have also been a few attempts to define*extensional**higher*-*order**logic**programming*systems. ...##
###
Extensional Higher-Order Logic Programming
[article]

2011
*
arXiv
*
pre-print

We propose a purely

arXiv:1106.3457v1
fatcat:qmgckht2ifbz3llo7kclbvjcxi
*extensional*semantics for*higher*-*order**logic**programming*. ... In other words, we provide a purely*extensional*theoretical framework for*higher*-*order**logic**programming*which generalizes the familiar theory of classical (first-*order*)*logic**programming*. ... Acknowledgments: We would like to thank Costas Koutras for valuable discussions regarding algebraic lattices and the reading group on*programming*languages at the University of Athens for many insightful ...##
###
Extensional Higher-Order Logic Programming
[chapter]

2010
*
Lecture Notes in Computer Science
*

We propose a purely

doi:10.1007/978-3-642-15675-5_10
fatcat:wttojqsxsbh2vayedz6wzd6leq
*extensional*semantics for*higher*-*order**logic**programming*. ... In other words, we provide a purely*extensional*theoretical framework for*higher*-*order**logic**programming*which generalizes the familiar theory of classical (first-*order*)*logic**programming*. ... There have also been a few attempts to define*extensional**higher*-*order**logic**programming*systems. ...##
###
Extensional Semantics for Higher-Order Logic Programs with Negation
[article]

2017
*
arXiv
*
pre-print

] to

arXiv:1701.08622v2
fatcat:7q3uzvlkpvf7bdas25m7g7mkhi
*higher*-*order**logic**programs*, does not in general lead to*extensional*stable models. ... We develop an*extensional*semantics for*higher*-*order**logic**programs*with negation, generalizing the technique that was introduced in [Bezem99,Bezem01] for positive*higher*-*order**programs*. ... in [6] to give the first*extensional*semantics for*higher*-*order**logic**programs*with negation. ...##
###
Minimum Model Semantics for Extensional Higher-order Logic Programming with Negation

2014
*
Theory and Practice of Logic Programming
*

AbstractExtensional

doi:10.1017/s1471068414000313
fatcat:np53agfr2jcijofn6elbi2m3jy
*higher*-*order**logic**programming*has been introduced as a generalization of classical*logic**programming*. ... Wadge in*order*to demonstrate the semantic difficulties of*higher*-*order**logic**programming*. ... Resolving a Semantic Paradox of*Higher*-*Order**Logic**Programming*One deficiency of*extensional**higher*-*order**logic**programming*is the inability to define rules (or facts) that have predicate constants in ...##
###
The Intricacies of 3-Valued Extensional Semantics for Higher-Order Logic Programs
[article]

2017
*
arXiv
*
pre-print

Bezem defined an

arXiv:1707.04704v1
fatcat:fm37nbydy5bsbmi42jmpgcudlu
*extensional*semantics for positive*higher*-*order**logic**programs*. ... On the positive side, we demonstrate that for stratified*higher*-*order**logic**programs*,*extensionality*is indeed achieved. ...*Extensional**Higher*-*Order**Logic**Programming*In (Wadge 1991) W. W. ...##
###
The Intricacies of Three-Valued Extensional Semantics for Higher-Order Logic Programs

2018
*
Proceedings of the Twenty-Seventh International Joint Conference on Artificial Intelligence
*

Bezem for providing

doi:10.24963/ijcai.2018/750
dblp:conf/ijcai/RondogiannisS18
fatcat:fptlqzo6xbhbnhy6l7icdpt6be
*extensional*semantics to positive*higher*-*order**logic**programs*, fails when applied to*higher*-*order**logic**programs*with negation. ... On the positive side, we demonstrate that for stratified*higher*-*order**logic**programs*,*extensionality*is indeed achieved by the technique. ...*Extensional**Higher*-*Order**Logic**Programming*In (Wadge 1991) W. W. ...##
###
A Normalizing Computation Rule for Propositional Extensionality in Higher-Order Minimal Logic

2018
*
Types for Proofs and Programs
*

Predicative

doi:10.4230/lipics.types.2016.3
dblp:conf/types/AdamsBC16
fatcat:r4sde5q3bnddhd7slorm4kn72y
*Higher*-*Order*Minimal*Logic*with*Extensional*Equality We call the following type theory PHOML, or predicative*higher*-*order*minimal*logic*with*extensional*equality. ... We 3:12 Propositional*Extensionality*in*Higher*-*Order*Minimal*Logic*Thus, the construction gives a proof of ⊃ ( ⊃ ) which, given two proofs of , selects the first. ... Conclusion and Future Work We have presented a system with propositional*extensionality*, and shown that it satisfies the property of canonicity. ...##
###
Page 8876 of Mathematical Reviews Vol. , Issue 2000m
[page]

2000
*
Mathematical Reviews
*

Some typical examples of

*higher*-*order**logic**programs*are shown to be*extensional*.” ... Summary: “We set up a framework for the study of*extensional*- ity in the context of*higher*-*order**logic**programming*. ...##
###
Extensional Collapse Situations I: non-termination and unrecoverable errors
[article]

2011
*
arXiv
*
pre-print

We consider a simple model of

arXiv:1101.4465v1
fatcat:kjnwhlevhfb5xkejlaq2kj4dqi
*higher**order*, functional computation over the booleans. ... We show that the models so defined form a lattice when*ordered*by the*extensional*collapse situation relation, introduced in*order*to compare models with respect to the amount of "intensional information ... Thanks to an anonymous referee of a previous version of this work, for suggesting that pre-*logical*relations are the proper framework to deal with*extensional*collapse situations. ...##
###
Hot: A concurrent automated theorem prover based on higher-order tableaux
[chapter]

1998
*
Lecture Notes in Computer Science
*

Hot is an automated

doi:10.1007/bfb0055140
fatcat:tuxfckgj5bao5awpbid6rhe2ha
*higher*-*order*theorem prover based on HT E, an*extensional**higher*-*order*tableaux calculus. ... We show the usefulness of the implementation by including benchmark results for over one hundred solved problems from*logic*and set theory. ...*programming*, constraint*logic**programming*, and concurrent objects with multiple inheritance Smo95] . ...##
###
A Calculus of Coroutines
[chapter]

2004
*
Lecture Notes in Computer Science
*

Games can capture precisely the behaviour of

doi:10.1007/978-3-540-27836-8_74
fatcat:hrcyftg22bcc3mw52qs3vbyr5y
*higher*-*order**programs*in sequential languages, in a fashion which is very difficult or impossible for traditional forms of denotational semantics. ... By contrast, in domain theory*programs*are modelled*extensionally*using sets (with certain*order*-theoretic structure) and functions (preserving that structure). ... Games can capture precisely the behaviour of*higher*-*order**programs*in sequential languages, in a fashion which is very difficult or impossible for traditional forms of denotational semantics. ...##
###
Higher-order algebra with transfinite types
[chapter]

1996
*
Lecture Notes in Computer Science
*

We extend the simple type system of

doi:10.1007/3-540-61254-8_29
fatcat:gknb7vdttzg25ni6s6mlqrc5nq
*higher*{*order*algebra with transnite types. ... We present a general model theory for transnite*higher*{*order*algebra including results on the existence and construction of free and initial models, and a sound and complete equational calculus. ... We show that transnite*higher*{*order*equational*logic*is both sound and complete with respect to*extensional*6, algebras. ...##
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Equivalence of two Fixed-Point Semantics for Definitional Higher-Order Logic Programs

2015
*
Electronic Proceedings in Theoretical Computer Science
*

Two distinct research approaches have been proposed for assigning a purely

doi:10.4204/eptcs.191.4
fatcat:v4pl3qvauzbapdkcsirk5rpasq
*extensional*semantics to*higher*-*order**logic**programming*. ... The results of the paper contribute to a better understanding of the semantics of*higher*-*order**logic**programming*. ... From the above examples it can be understood that*extensional**higher*-*order**logic**programming*sacrifices some of the rich syntax of intensional*higher*-*order**logic**programming*in*order*to achieve semantic ...##
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Page 5241 of Mathematical Reviews Vol. , Issue 98H
[page]

1998
*
Mathematical Reviews
*

for

*higher*-*order*terms in y-long B-normal form (108-122); Roberto Virga,*Higher*-*order*superposition for dependent types (123-137). ... Contents: Chitta Baral, Relating*logic**programming*theories of actions and partial*order*planning (131-151); Howard A. ...
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