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Extensional Higher-Order Logic Programming

Angelos Charalambidis, Konstantinos Handjopoulos, Panagiotis Rondogiannis, William W. Wadge
2013 ACM Transactions on Computational Logic  
We propose a purely 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.  ... 
doi:10.1145/2499937.2499942 fatcat:ek66hrnijjawbofxnnnq4ymksq

Extensional Higher-Order Logic Programming [article]

A. Charalambidis, K. Handjopoulos, P. Rondogiannis, W. W. Wadge
2011 arXiv   pre-print
We propose a purely 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  ... 
arXiv:1106.3457v1 fatcat:qmgckht2ifbz3llo7kclbvjcxi

Extensional Higher-Order Logic Programming [chapter]

Angelos Charalambidis, Konstantinos Handjopoulos, Panos Rondogiannis, William W. Wadge
2010 Lecture Notes in Computer Science  
We propose a purely 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.  ... 
doi:10.1007/978-3-642-15675-5_10 fatcat:wttojqsxsbh2vayedz6wzd6leq

Extensional Semantics for Higher-Order Logic Programs with Negation [article]

Panos Rondogiannis, Ioanna Symeonidou
2017 arXiv   pre-print
] to 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.  ... 
arXiv:1701.08622v2 fatcat:7q3uzvlkpvf7bdas25m7g7mkhi

Minimum Model Semantics for Extensional Higher-order Logic Programming with Negation

ANGELOS CHARALAMBIDIS, ZOLTÁN ÉSIK, PANOS RONDOGIANNIS
2014 Theory and Practice of Logic Programming  
AbstractExtensional 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  ... 
doi:10.1017/s1471068414000313 fatcat:np53agfr2jcijofn6elbi2m3jy

The Intricacies of 3-Valued Extensional Semantics for Higher-Order Logic Programs [article]

Panos Rondogiannis, Ioanna Symeonidou
2017 arXiv   pre-print
Bezem defined an 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.  ... 
arXiv:1707.04704v1 fatcat:fm37nbydy5bsbmi42jmpgcudlu

The Intricacies of Three-Valued Extensional Semantics for Higher-Order Logic Programs

Panos Rondogiannis, Ioanna Symeonidou
2018 Proceedings of the Twenty-Seventh International Joint Conference on Artificial Intelligence  
Bezem for providing 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.  ... 
doi:10.24963/ijcai.2018/750 dblp:conf/ijcai/RondogiannisS18 fatcat:fptlqzo6xbhbnhy6l7icdpt6be

A Normalizing Computation Rule for Propositional Extensionality in Higher-Order Minimal Logic

Robin Adams, Marc Bezem, Thierry Coquand, Michael Wagner
2018 Types for Proofs and Programs  
Predicative 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.  ... 
doi:10.4230/lipics.types.2016.3 dblp:conf/types/AdamsBC16 fatcat:r4sde5q3bnddhd7slorm4kn72y

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]

Antonio Bucciarelli
2011 arXiv   pre-print
We consider a simple model of 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.  ... 
arXiv:1101.4465v1 fatcat:kjnwhlevhfb5xkejlaq2kj4dqi

Hot: A concurrent automated theorem prover based on higher-order tableaux [chapter]

Karsten Konrad
1998 Lecture Notes in Computer Science  
Hot is an automated 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] .  ... 
doi:10.1007/bfb0055140 fatcat:tuxfckgj5bao5awpbid6rhe2ha

A Calculus of Coroutines [chapter]

J. Laird
2004 Lecture Notes in Computer Science  
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.  ...  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.  ... 
doi:10.1007/978-3-540-27836-8_74 fatcat:hrcyftg22bcc3mw52qs3vbyr5y

Higher-order algebra with transfinite types [chapter]

L. J. Steggles
1996 Lecture Notes in Computer Science  
We extend the simple type system of 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.  ... 
doi:10.1007/3-540-61254-8_29 fatcat:gknb7vdttzg25ni6s6mlqrc5nq

Equivalence of two Fixed-Point Semantics for Definitional Higher-Order Logic Programs

Angelos Charalambidis, Panos Rondogiannis, Ioanna Symeonidou
2015 Electronic Proceedings in Theoretical Computer Science  
Two distinct research approaches have been proposed for assigning a purely 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  ... 
doi:10.4204/eptcs.191.4 fatcat:v4pl3qvauzbapdkcsirk5rpasq

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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