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Formalizing a Constraint Deductive Database Language Based on Hereditary Harrop Formulas with Negation
[chapter]
Functional and Logic Programming
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In this paper, we present an extension of the scheme HH(C) (Hereditary Harrop formulas with Constraints) with a suitable formulation of negation in order to obtain a constraint deductive database query ...
We define a proof theoretic semantic framework based on a sequent calculus, that allows to represent the meaning of a database query by means of a derived constraint answer in the sense of CLP. ...
Introduction The scheme HH(C) (Hereditary Harrop formulas with Constraints) [10] extends HH by adding constraints, in a similar way the extension of LP (Logic Programming) with constraints gave rise ...
doi:10.1007/978-3-540-78969-7_21
dblp:conf/flops/NievaSS08
fatcat:j4sk43eh3fer5anyxgli7yi234
Implementing a fixed point semantics for a constraint deductive database based on hereditary harrop formulas
2009
Proceedings of the 11th ACM SIGPLAN conference on Principles and practice of declarative programming - PPDP '09
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This work is aimed to show a concrete implementation of a deductive database system based on the scheme HH¬(C) (Hereditary Harrop Formulas with Negation and Constraints) following a fixpoint semantics ...
We have developed a Prolog implementation for this scheme that is constraint system independent, therefore allowing to use it as a base for any instance of the formal scheme. ...
used in our finite domain constraint solver. ...
doi:10.1145/1599410.1599426
dblp:conf/ppdp/Aranda-LopezNSS09
fatcat:fp74dpsfo5fpjepfar2elceecu
A Survey of the Proof-Theoretic Foundations of Logic Programming
[article]
2021
arXiv
pre-print
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Anchoring logic programming in proof theory has also helped identify its connections and differences with functional programming, deductive databases, and model checking. ...
Several formal systems, such as resolution and minimal model semantics, provide a framework for logic programming. ...
Acknowledgments: I thank Miroslaw Truszczynski and several anonymous reviewers for their comments on an earlier version of this paper. ...
arXiv:2109.01483v2
fatcat:fp3c746m5zaavd56ltn2d43kp4
Reference List of Indexed Articles
2002
The Journal of Logic and Algebraic Programming
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Harland, Success and Failure for Hereditary Harrop Formulae 17 (1) (1993) 1-29 240. H.-P. Ko, D. McAllester and M.E. Nadel, Lower Bounds for the Lengths of Refutations 17 (1) (1993) 31-58 241. G. ...
Tsur, Set Constructors in a Logic Database Language 10 (1-4) (1991) 181-232 149. J.F. Naughton and Y. ...
doi:10.1016/s1567-8326(01)00020-0
fatcat:qoxvtgq6lngblb74znc4gj2yfm
Modular logic metaprogramming
2010
Proceedings of the ACM international conference on Object oriented programming systems languages and applications - OOPSLA '10
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In logic metaprogramming, programs are not stored as plain textfiles but rather derived from a deductive database. ...
We have formalized the resulting module system and have proven the soundness of separate checking. ...
Formally, the set ofF P + formulas is a subset of the firstorder hereditary Harrop formulas (fohh) [32] , and the proof method (which was sketched in the motivation in Sec. 3) for fohh agrees with the ...
doi:10.1145/1869459.1869499
dblp:conf/oopsla/KloseO10
fatcat:bemdzqhczvbtjbybha2foyxj6i
Modular logic metaprogramming
2010
SIGPLAN notices
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In logic metaprogramming, programs are not stored as plain textfiles but rather derived from a deductive database. ...
We have formalized the resulting module system and have proven the soundness of separate checking. ...
Formally, the set ofF P + formulas is a subset of the firstorder hereditary Harrop formulas (fohh) [32] , and the proof method (which was sketched in the motivation in Sec. 3) for fohh agrees with the ...
doi:10.1145/1932682.1869499
fatcat:7s6bnjuyfja2rpmdvuhf4vtvcq
On the use of advanced logic programming languages in computational linguistics
1995
The Journal of Logic Programming
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Moreover, it raises the context to the formula level, allowing reasoning based on the deduction rules of intuitionistic logic. ...
We have also presented a Logic Grammar formalism derived from the clause language of AProlog: higher-order hereditary Harrop grammars. ...
doi:10.1016/0743-1066(95)00040-q
fatcat:ph7ll7eoinekvll3i6o5ktyqsa
Automated deduction for verification
2009
ACM Computing Surveys
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A logic consists of a formal language, a formal semantics, and a formal proof system. ...
Language and Semantics. For our purpose, a propositional formula φ is either an atom from a set A of atoms, a negation ¬φ 1 , or a disjunction φ 1 ∨φ 2 . ...
Bill Mc-Cune and Matt Kaufmann responded with clarifications on specific points. ...
doi:10.1145/1592434.1592437
fatcat:satgicglyneqvl2nw5pjnr3d3a
Restricted Predicates for Hypothetical Datalog
2015
Electronic Proceedings in Theoretical Computer Science
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A former work introduced both a formal framework and a goal-oriented tabled implementation, allowing negation in rule bodies. ...
Hypothetical Datalog is based on an intuitionistic semantics rather than on a classical logic semantics, and embedded implications are allowed in rule bodies. ...
A more recent work [1] proposes HH ¬ (C) as a constraint database framework including negation, but with no negative assumptions. ...
doi:10.4204/eptcs.200.5
fatcat:ylgwqaal6rfmfadlhwwymt2bs4
Applications of Linear Logic to Computation: An Overview
1994
Logic Journal of the IGPL
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A very complete yet brief reference of LL theory is 136]. Unfortunately it is in Japanese, but one can still read the formulas. No references are included. ...
on LL to date), and a good book on proof-theoretical issues and their computational interpretation is Proofs and Types 73]. ...
I am especially indebted to Narciso for correcting a number of typos. I am grateful to Andrea Asperti for pointing me out the work on optimal lambda reduction. ...
doi:10.1093/jigpal/2.1.77
fatcat:gezeeaim4rfqpeikikhcip44eu
A logical analysis of modules in logic programming
1989
The Journal of Logic Programming
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We also examine a weak notion of negation which is easily implemented in this language and show how database constraints can be represented by it. a IMPLICATIONS AS GOALS We shall assume that our logical ...
language is a first-order language with denumerably many constants, variables, functions symbols, and predicates (at all arities). ...
Hereditary Harrop formulas can be defined for both first-order and higher-order logic. Gabbay and Reyle in [7] have described a logical language very similar to the one presented here. ...
doi:10.1016/0743-1066(89)90031-9
fatcat:pwoqnqqxafbgdgc3d4ttkyfl7q
Finitary partial inductive definitions as a general logic
[chapter]
1994
Lecture Notes in Computer Science
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In the deductive approach, the logic is defined by its inference rules. Only the succedent rules (in a sequent calculus setting -introduction rules in a natural deduction setting) need be given. ...
The latter approach often provides a more straightforward representation of logics with simple semantics but complicated proof systems. ...
Since our metalogic (extended with logical variables as in [6] ) can be regarded as a superset of the higher-order hereditary Harrop languages of the ~Prolog family, all of Felty's specifications can ...
doi:10.1007/3-540-58025-5_52
fatcat:r4zaqenrdbg6bpxypidork3c4q
Elimination of Negation in a Logical Framework
[chapter]
2000
Lecture Notes in Computer Science
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fragment of higher-order hereditary Harrop formulae. ...
Logical frameworks with a logic programming interpretation such as hereditary Harrop formulae cannot directly express negative information, although negation is a useful specification tool. ...
algorithm for a useful class of third-order hereditary Harrop formulae. ...
doi:10.1007/3-540-44622-2_28
fatcat:hywfda5dhfhtdgf2lmigtjz4om
The Cognitive Programming Paradigm the Next Programming Struture
2013
American Journal of Software Engineering and Applications
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The various programming languages stem from the difficulties man has in using one programming language to solve different problems on the computer. ...
This approach could lift the burden on Managers and Executives in deliberating further on results of a processed business problem. ...
,Horn clauses or Hereditary Harrop formulas. As in the purely declarative case, the programmer is responsible for ensuring the truth of programs. ...
doi:10.11648/j.ajsea.20130202.15
fatcat:wwuqsgv2yjgozpp5idtqf7t25i
Higher-order logic programming
[chapter]
1986
Lecture Notes in Computer Science
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We are grateful to Gilles Dowek for his comments on this chapter. ...
(i) Σ; P O , (ii) Σ; P O A where A The main novelty from a programming perspective of a language based on hereditary Harrop formulas over one based on Horn clauses is the following: in the new language ...
The possibility for universal quantifiers to appear in goal formulas with their associated semantics leads to such a capability being present in a language based on higher-order hereditary Harrop formulas ...
doi:10.1007/3-540-16492-8_94
fatcat:zcqxdnpzhbglnfez7h3ih5xsgi
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