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Formalizing a Constraint Deductive Database Language Based on Hereditary Harrop Formulas with Negation [chapter]

Susana Nieva, Jaime Sánchez-Hernández, Fernando Sáenz-Pérez
Functional and Logic Programming  
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

Gabriel Aranda-López, Susana Nieva, Fernando Sáenz-Pérez, Jaime Sánchez-Hernández
2009 Proceedings of the 11th ACM SIGPLAN conference on Principles and practice of declarative programming - PPDP '09  
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]

Dale Miller
2021 arXiv   pre-print
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  
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

Karl Klose, Klaus Ostermann
2010 Proceedings of the ACM international conference on Object oriented programming systems languages and applications - OOPSLA '10  
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

Karl Klose, Klaus Ostermann
2010 SIGPLAN notices  
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

Solange Coupet-Grimal, Olivier Ridoux
1995 The Journal of Logic Programming  
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

Natarajan Shankar
2009 ACM Computing Surveys  
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

Fernando Sáenz-Pérez
2015 Electronic Proceedings in Theoretical Computer Science  
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

VLADIMIR ALEXIEV
1994 Logic Journal of the IGPL  
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

Dale Miller
1989 The Journal of Logic Programming  
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]

Lars -Henrik Eriksson
1994 Lecture Notes in Computer Science  
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]

Alberto Momigliano
2000 Lecture Notes in Computer Science  
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

Benjamin Odei Bempong
2013 American Journal of Software Engineering and Applications  
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]

Dale A. Miller, Gopalan Nadathur
1986 Lecture Notes in Computer Science  
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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