The discussion of the foundations also facilitates a systematic survey of variants of the logic programming scheme, like constraint logic programming, deductive databases or concurrent logic programming. Horn lp is the foundation of logic programming and prolog 1. Use sldresolution to show that the resulting set of horn clauses is inconsistent see page 48 of the logic and resolution chapter for a description of sld resolution. Logic programming is most commonly understood in a restricted sense, namely, programming with horn clauses and sld resolution. Declarative programming vrije universiteit brussel. Sldresolution calculus, in a \direct way and closely to the style of classical logic programming, this is a revised version of \l.
Download free book logic, programming and prolog 2nd edition by by ulf nilsson and jan maluszynski in pdf format. Mar 16, 2009 download free book logic, programming and prolog 2nd edition by by ulf nilsson and jan maluszynski in pdf format. The use of logic as the basis for program development is motivated by the possibilities it offers for achieving greater program correctness. A fixpoint semantics and an sld resolution calculus for modal logic programs. There is for practical purposes only one working programming language, prolog, that can be considered as a significant realization of the logic programming paradigm. Logic programming sld treesgrandfathera,xparentb,xfatherb,x motherb,x blockedfathera,e,parente,x every. We provide a rigorous semantics for logic programs, and show the correctness and completeness of sldresolution with respect to this semantics. The foundations of horn programming and sldresolution with built in predicates are investigated in 1. Let us be very clear about what is being claimed here. Hauskrecht administration homework assignment 2 propositional logic exercises programming a resolution solver. A fixpoint semantics and an sldresolution calculus for modal logic programs. A further contribution of this thesis is the rediscovery of fair sldresolution as a fundamental way to guarantee termination of compositional programs within the con nes of resolution. In fact, prolog implementation will try these choices out exhaustively in a depth. This is achieved by amalgamating sld resolution, cosld resolution, and constraint logic programming in a single logic programming system.
Logic programming and prolog institute for computing and. We propose a new typetheoretic approach to sldresolution and hornclause logic programming. Free pdf download logic, programming and prolog 2nd edition. Sld resolution horn clauses, sld resolution, logic programming. Logic for computer scientistspredicate logicstrategies for. Soundness and completeness of this rule are discussed. We will now focus on resolution for a single goal clause and a definite program. A fixpoint semantics and an sldresolution calculus for. A search rule is a rule for choosing a clause in the program to resolve with the chosen literal in a goal clause. This is based on the principle of coinduction, which is in turn based on the ability to. It views horn formulas as types, and derivations for a given query as a construction of the inhabitant a proofterm for the type given by the query. Main logic programming ideas logic programming underlies configassure, mulvaland rapidnet a logic program is a set of definiteclauses of the form a b0,b k, k.
Two literals are said to be complements if one is the negation of the other in the following. Sldresolution because 1 most forms of ilp learn definite logic programs typically. We want to show that whenever we can find a sld refutation from a definite program p plus a goal g, then g is a logical consequence of p, i. Structural resolution for logic programming ceur workshop. Let p be a definite program and g 0 be a definite goal. A horn clause is a disjunction of literals containing at most one positive literal. We prove that our sldresolution calculus is sound and complete. Sldresolution and logic programming prolog ftp directory. Most of the experiments are short and to the point, just like traditional homework problems, so that they reflect the daily classroom work.
Lecture notes in computer science lecture notes in artificial intelligence, vol 1228. Resolution and logic programming slide 1 cs3234 logic and formal systems lecture 05 090904 ground resolution uni. Sld resolution symbolic logic and logic processing. In logic programming, the control over the execution of the program is completely supplied by the resolution engine compiler and is said to be uniform control, realized by. We develop semantics for modal logic programs in basic serial multimodal logics, which are parameterized by an arbitrary combination of generalized versions of axioms t, b, 4, 5 in the form, e. In these books, these results are established for the horn clause logic of prolog in chapters 5 to 7. Unfortunately, though, fair sldresolution using the breadth rst computation rule exhibits e ciency behaviour that is di cult to predict.
In algorithmic programming, the programmer has effective control over program execution, generally through. Disjunctive logic programming, sldresolution, proof procedure. Prolog experiments in discrete mathematics, logic, and. Sld resolution selective linear definite clause resolution is the basic inference rule used in logic programming.
Sldresolution, which is a central algorithm for logic programming, takes a goal g, typically written as. On sldnfresolution in logic programming with negation. In logic programming in general we have to define addition in the proper recursive way. The use of negation in logic programming is discussed in chapter 4. Use sld resolution to show that the resulting set of horn clauses is inconsistent see page 48 of the logic and resolution chapter for a description of sld resolution. It is through the inference rule of resolution that both proofs and computations can be manipulated on computers, and this book contains. Compositional logic programming richard mcphee worcester college submitted for the degree of doctor of philosophy trinity term 2000 abstract.
The field of logic programming is fortunate in being well served by many excellent books covering virtually every aspect of the subject, including its theory, applications and programming. This note will explain the connection between logic and computer programming using horn clauses and a special type of resolution, namely sld resolution. An sldresolution calculus for basic serial multimodal. Oct 30, 2011 the relevance of horn clauses to theorem proving by firstorder resolution is that the resolution of two horn clauses is a horn clause.
Sld resolution forward and backward chaining efficiency of reasoning with horn clausesefficiency of reasoning with horn clauses horn fol vs horn lp. Propositional logic exercises programming a resolution solver. The aim of this thesis is to define a procedural and declarative semantics of sld resolution with reflection, in the general framework defined by jaffar et al. Logic programming and resolution lecture notes for inf31704171 leif harald karlsen autumn 2015 1 introduction this note will explain the connection between logic and computer programming using horn clauses and a special type of resolution, namely sld resolution. Sldresolution reduction of secondorder horn fragments. The resolution rule in propositional logic is a single valid inference rule that produces a new clause implied by two clauses containing complementary literals. An sldresolution calculus for basic serial multimodal logics. For sets of horn clauses, there is a variant of resolution called sldresolution, which. Shepherdson, sldnf resolution with equality, journal of automated reasoning 8. Msc module cs612 automated reasoning prolog, resolution and logic programming alan williams room 2. Firstorder logic allow the representation of entities also called objects and their properties, and relations among such entities more expressive than propositional logic.
Resolution is sound and complete with respect to propositional symbols for the kbs in the horn normal. Prologs sldresolution engine finds the solutions to this query namely, x pi, x sj, by direct match pi and one resolution step sj using the rule translating the information that a student is also a person and then matching on the student sj who has property prop. Logic for computer scientistspredicate logicstrategies. Automated theorem proving is increasingly used in the. Main difference between logic programming and ordinary algorithmic programming. By contrast, there are extensions of sldresolution and standard resolution that handle the full expressivity of higherorder logic 7,23. We want to show that for a definite program p plus a.
A logic programming language with builtin inheritance hassan aitkaci and roger nasr d an elaboration of the prolog language is described in which the notion of firstorder term is replaced by a more general one. Free pdf download logic, programming and prolog 2nd. The aim of this thesis is to define a procedural and declarative semantics of sldresolution with reflection, in the general framework defined by jaffar et al. Sldresolution suppose p is a set of program clauses, r the computation rule, and g a goal clause.
Sld refutation tree you may have noticed that in sld resolution there may be multiple choices for the program factrule. Given that parallelism in logic programs can be implicitly exploited 8, complex, computeintensive applications planning, scheduling. An introduction to logic programming through prolog. We want to show that whenever we can find a sldrefutation from a definite program p plus a goal g, then g is a logical. This mathematically oriented introduction to the theory of logic programming presents a systematic exposition of the resolution method for propositional, firstorder, and horn clause logics, together with an analysis of the semantic aspects of the method. It is a refinement of resolution, which is both sound and refutation complete for horn clauses. Sld resolution, which is a central algorithm for logic programming, takes a goal g, typically written as. There is also a general resolution for full clause logic, but for. Sldresolution on secondorder clauses, as used in this paper, supports the uni. The relevance of horn clauses to theorem proving by firstorder resolution is that the resolution of two horn clauses is a horn clause. Sldresolution, selects literals in a goal from those whose resolution is known to terminate at the expense of the others.
A fixpoint semantics and an sldresolution calculus for modal. A literal is a propositional variable or the negation of a propositional variable. C1 using sldresolution because it is impossible to derive a clause with. This book contains programming experiments that are designed to reinforce the learning of discrete mathematics, logic, and computability. In the 1990s, research in logic programming focused on making the basic principle more expressive by including constraints equations and inequalities over arithmetic domains, which gave rise to constraint logic programming. Multisld resolution is a variant of sld resolution based on a simple idea let the allowed constraints be closed under disjunction, and provide a mechanism for collecting solutions to a goal and. Automated reasoning, deep learning, logic programming, resolution, neural networks. Disjunctive logic programming, sld resolution, proof procedure. Linear resolution with selection function for definite clauses. Translate this set of clauses to the horn clause notation as used in logic programming. All prolog examples are compatible with swiprolog free software. This chapter introduces the inference mechanism which is the basis of most logic programming systems. We provide a rigorous semantics for logic programs, and show the correctness and completeness of sld resolution with respect to this semantics.
Multi sld resolution is a variant of sld resolution based on a simple idea let the allowed constraints be closed under disjunction, and provide a mechanism for collecting solutions to a goal and. Jean gallier, sld resolution and logic programming chapter 9 of logic for computer science. Prologs sldresolution engine finds the solutions to this query namely, x pi, x sj. Logic programming in prolog part ii substitutions, sld. Sld resolution because 1 most forms of ilp learn definite logic programs typically. Depthfirst search wikipedia breadthfirst search wikipedia redefinition of prolog append3 using the function cons2 a note. We propose a method of program transformation that allows to transform logic programs in. Foundations of automatic theorem proving, 2003 online revision free to download, originally published by wiley, 1986. We do not claim to have defined a fundamentally new form of sld resolution with equality.
1348 857 130 1046 947 441 1274 1373 533 1201 1344 1561 564 683 1466 655 589 1367 299 725 1200 1478 382 10 303 837 717 459 787 1544 379 1497 174 976 152 335 1300 603 255 541 1222 833 1230 619 346 434 243 735 717 125