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Applying SLD-Resolution to a Class of Non-Horn Logic Programs

GRIGORIS ANTONIOU, ELMAR LANGETEPE
1994 Logic Journal of the IGPL  
The result can be applied to default reasoning and has some relevance for model elimination based theorem proving. 230 Applying SLD-Resolution to a Class of Non-Horn Logic Programs The main idea of our  ...  Then, the tranformed knowledge base is again a de nite logic program, and we may use SLD-resolution. Of course, we must take care that p is treated as :p. This is done by contrapositions of rules.  ...  of a model-based proof of Theorem 2.3.  ... 
doi:10.1093/jigpal/2.2.229 fatcat:7vlvtlp625ddplcheafhfffmam

Heterogeneous SLD resolution

Lee Naish
1984 The Journal of Logic Programming  
The soundness of HSLD resolution is a direct consequence of the soundness of SLD resolution, since HSLD branches are, in essence, no different from SLD branches.  ...  THEORETICAL RESULTS In [lo] appears the most concise proof of the soundness and completeness of SLD resolution, with respect to success and finite failure (finite failure completeness is subject to a fairness  ... 
doi:10.1016/0743-1066(84)90027-x fatcat:daylm32o2rf6zckdcccjoxxykq

Productive Corecursion in Logic Programming [article]

Ekaterina Komendantskaya, Yue Li
2017 arXiv   pre-print
Logic Programming is a Turing complete language.  ...  For example, the existing state-of-the-art algorithms can only semi-decide coinductive soundness of queries in logic programming for regular formulae.  ...  The other direction is proven trivially from the operational equivalence of infinite S-resolution and SLD-resolution derivations. Proof 1.  ... 
arXiv:1707.01541v4 fatcat:oaepf7ppybd4lmjjb2svb6phi4

Recursive query processing: the power of logic

Laurent Vielle
1989 Theoretical Computer Science  
The purpose of this paper is to show that a computational model developed in the framework of resolution provides a very adequate tool to study and develop query answering procedures for deductive databases  ...  To achieve our goal, we first develop techniques (applicable to general logic programs) for the construction of abstract search spaces associated with a query, and we discuss their properties.  ...  Acknowledgment It is a pleasure to acknowledge the support and the advice of Jean-Marie Nicolas.  ... 
doi:10.1016/0304-3975(89)90088-1 fatcat:nzvemudlq5gfhbgbkk2gl6qghy

Structural Resolution: a Framework for Coinductive Proof Search and Proof Construction in Horn Clause Logic [article]

Ekaterina Komendantskaya, Patricia Johann, Martin Schmidt
2017 arXiv   pre-print
One algorithm combines the method of loop detection with productive structural resolution, thus guaranteeing productivity of coinductive proofs for infinite rational terms.  ...  Structural resolution is a newly proposed alternative to SLD-resolution that makes it possible to define and semi-decide a notion of productivity appropriate to LP.  ...  We particularly thank Vladimir Komendantskiy and Frantiŝek Farka, who at different times implemented prototypes of CoAlgebraic Logic Programming (CoALP) and S-Resolution: their input has been invaluable  ... 
arXiv:1511.07865v2 fatcat:6lqbu7vyqzegnchxtiws7ty3fu

Contributions to the Theory of Logic Programming

Krzysztof R. Apt, M. H. van Emden
1982 Journal of the ACM  
A semantic characterization of finite failure of SLD-resolution is given, which coincides with the greatest fixpoint only for a special case of clauses.  ...  The first completeness proof is due to Hill (9). This proof does not apply the fix.point technique.  ...  If A is in the least model of P, then/or some k, -A is k-refutab/e. PROOF. Analogous to the proof of Lemma 5.5 using Lemma 6.4. D THEOREM 6.6 (STRONG COMPLETENESS OF SLD-RESOLUTION).  ... 
doi:10.1145/322326.322339 fatcat:7t3xpnxd35f33amqpnihtvymda

Page 6441 of Mathematical Reviews Vol. , Issue 2004h [page]

2004 Mathematical Reviews  
The defined fixpoint semantics and the corresponding SLD-resolution calculus are designed in a style similar to that of classical logic programming, and are proved to be sound and complete.  ...  A fixpoint semantics and an SLD-resolution calculus are provided for all of the basic serial modal logics KD, T, KDB, B, KD4, S4, KD5S, KD45, and SS.  ... 

Running programs backwards: The logical inversion of imperative computation

Brian J. Ross
1997 Formal Aspects of Computing  
Program relations denote both forward and backward computations, and the direction of the computation depends upon the instantiation pattern of arguments in the relation.  ...  This view of inversion has practical applications when the relational semantics is treated as a logic program.  ...  Acknowledgements: Thanks to Harvey Abramson for his supervision of my MSc thesis, of which this work is a direct extension; Rajiv Trehan for his advice on CLP languages; Jamie Andrews, Rob Scott and Paul  ... 
doi:10.1007/bf01211087 fatcat:ukqpndvu4fe6pbjod7tplanspq

Regular search spaces as a foundation of logic programming [chapter]

Alberto Momigliano, Mario Ornaghi
1994 Lecture Notes in Computer Science  
Secondly, we embark on a generalization and abstraction of the nice properties of SLD-resolution. The outcome is our formulation of the concept of regular search space.  ...  First, we aim to provide a proof-theoretic reconstruction of logic programming, both for definite and for normal programs.  ...  We would like to thank Roy Dyckhoff and Frank Pfenning for their valuable comments on earlier versions of this paper.  ... 
doi:10.1007/3-540-58025-5_59 fatcat:7okk6khlq5gozo7wydffw5hqxe

Some issues and trends in the semantics of logic programming [chapter]

J. Jaffar, J -L. Lassez, M. J. Maher
1986 Lecture Notes in Computer Science  
In the first part we will review the main semantic properties of definite clauses, which form a theoretical basis for the study of PROLOG.  ...  A major problem facing the designers of programming languages is the conflict between expressive power (or "high-levelness") and efficiency of execution.  ...  Acknowledgements: The support from IBM Australia is gratefully acknowledged and we thank the text consultants at Yorktown Heights for their advice.  ... 
doi:10.1007/3-540-16492-8_78 fatcat:ly6owdbvyrdszkrao3u5hx2w4u

On Greatest Fixpoint Semantics of Logic Programming

M. Jaume
2002 Journal of Logic and Computation  
From Ä, we can define the following sequence of resolution steps: ß ß ( ß denotes the variables used for the renaming during the previous transitions).  ...  This reading leads into considering derivations as proofs rather than computations and allows one to show that for the subclass of infinite derivations over the domain of finite terms, a complete greatest  ...  Acknowledgements Many thanks to René Lalement, Catherine Dubois and Baudouin Le Charlier for enlightening discussions about this work, as well as the anonymous referees for some very useful comments.  ... 
doi:10.1093/logcom/12.2.321 fatcat:r6qj3gly45gpvc3wtntykmwgre

Crucial components in probabilistic inference pipelines

Dimitar Shterionov, Gerda Janssens
2015 Proceedings of the 30th Annual ACM Symposium on Applied Computing - SAC '15  
Due to the efficiency of the SLG (or SLD) resolution the grounding has little impact on the overall performance. Nested tries encode a disjunction of the collected proofs, i.e. a formula in DNF.  ...  A proof is a conjunction of literals derived by traversing the SLD tree starting from the root, i.e., the query, and ending at an empty clause.  ... 
doi:10.1145/2695664.2696006 dblp:conf/sac/ShterionovJ15 fatcat:z2xoj2atkbbgrhgvebvc4ye5ru

ON THE PROPOSITIONAL SLDNF-RESOLUTION

JAN A. PLAZA
1996 International Journal of Foundations of Computer Science  
We de ne notions of constructive transformation and constructive completion of a program.  ...  instead of multivalued semantics for the original program.  ...  Acknowledgments I would like to express my thanks to NSF for partial support of this research with grant IRI 9308970.  ... 
doi:10.1142/s0129054196000269 fatcat:6uka5ltzhjestbvvwdhimu6je4

Magic Sets vs. SLD-Resolution [chapter]

Stefan Brass
1996 Workshops in Computing  
We show that this happens only for tail-recursive programs, and that the only problem of magic sets is the materialization of "lemmas". So magic sets are always "as goal-directed as" SLD-resolution.  ...  There are a number of formalizations of this in the literature.  ...  Proof: By the completeness of SLD-resolution, there is an SLD-refutation A 1 , ψ 2 , . . . , ψ n , 2 with applied substitutions θ 1 , . . . , θ n such that θ 1 • · · · • θ n restricted to the variables  ... 
doi:10.1007/978-1-4471-1486-4_13 dblp:conf/adbis/Brass95 fatcat:u4wa5avwfnhhhgop7c5fvp36wi

Partial evaluation in logic programming

J.W. Lloyd, J.C. Shepherdson
1991 The Journal of Logic Programming  
For the procedural semantics, we show that, if P' U {G) is A-closed and A is independent, then P' is sound and complete wrt P for the goal G.  ...  We study, for both the declarative and procedural semantics, conditions under which P' is sound and complete wrt P for the goal G.  ...  So, if the clause C is the resultant of an SLDNF-derivation from + A, then the resultant of SLD-resolution on +-A using C is C. PROOF.  ... 
doi:10.1016/0743-1066(91)90027-m fatcat:xlmf5uqv6faipgif3yyw3p6v2a
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