J.H. Andrews. A Logical Semantics for Depth-first Prolog with Ground Negation. In D. Miller, editor, Proc.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....[4 7,9,10,17] When dealing with computational issues, one has to abandon classical 2 valued logic and has to move to multiple valued logic. A first attempt is to adopt a 3 valued logic where the third truth value (undefined) is introduced to model non terminating computations (see, e.g. [1,2,14,16,19]) However, these 3 valued based semantics do not allow to model the computational behaviour of Prolog. 1 Work partially supported by the EEC Project KIT011 LPKRR Preprint submitted to Elsevier Science 24 March 1997 In this paper we propose a logical semantics for pure Prolog (without ....

....are defined for pure logic programming, that is they model an operational behaviour based on SLD trees built by a fair computation rule and visited by a breadth first strategy. Recall that a fair computation rule is such that any (instance of) atom occurring in a goal is eventually selected. In [2], a semantics for Prolog in a logical style is presented. This logical semantics is proved correct with respect to an operational one, which essentially mimics the left to right depth first visit of a Prolog tree. The left to right depth first search rule is taken into account by using the ....

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J.H. Andrews. A Logical Semantics for Depth-first Prolog with Ground Negation. In D. Miller, editor, Proc.

....a logic program, then the goal r(t) terminates under the Prolog depth first search for every list t. The usefulness of the inductive extension is shown with a non trivial example program from the field of parsing. This article is an extended version of [28] 2 Related work Andrews introduces in [1] a logical semantics for depth first Prolog which is based on fold unfold transformations. Apt and Pedreschi study in [5] the termination of logic programs under the Prolog selection rule. They introduce the notion of acceptable programs and prove that acceptable 2 programs and bounded goals ....

J. Andrews. A logical semantics for depth-first Prolog with ground negation. Theoretical Computer Science, 184(1,2):105--143, 1997.

....(cf. e.g. 2, 4, 9, 16, 18] Our approach, however, is di#erent in two aspects. First, we have one single formal system in which we prove all the di#erent properties of logic programs. Second, we prove the properties not on the operational level but on the declarative level. The main di#erence to [1, 10, 14] is that we use classical logic. There are several di#erences between this article and [13, 21] In this article we use general goals and not only sequences of literals. This allows a uniform treatment of built in predicates including the predicate call n 1. The notion of modes, mode assignments ....

J. Andrews. A logical semantics for depth-first Prolog with ground negation. Theoretical Computer Science, 184(1,2):105--143, 1997.

....goals under Prolog. 1 Introduction The idea of transforming a propositional Prolog program into a logical theory that reflects the procedural behavior of the program is not new. Several transformations have been proposed for this purpose. Most of them are based on non classical logics. Andrews [1] uses folding unfolding transformations. Van Benthem [18] and Kalsbeek [11] capture computation mechanisms like standard Prolog with substructural Gentzen type calculi. Substructural means that certain classical structural rules are omitted or modified. Cerrito [5] transforms logic programs into ....

....since there are no clauses defining B 2 . Thus FB 2 is true. Together we obtain FB 1 # (S B 1 #FB 2 ) But we do not have F(B 1 , B 2 ) since the goal B 1 , B 2 loops in Prolog. In Prolog the atom B 1 is called loop and the atom B 2 is called fail . This example has also been studied in [1]. The failure of B 1 , B 2 can correctly be expressed as follows: either B 1 fails or B 1 terminates and B 2 fails. This corresponds to the formula FB 1 #(TB 1 #FB 2 ) where a new operator T is used describing termination of atoms. In rule (M i ) we see that in order to express the success ....

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J. Andrews. A logical semantics for depth-first Prolog with ground negation. Theoretical Computer Science, 184(1,2):105--143, 1997.

....Many valued logics have been employed in several studies of the semantics of logic programs. In particular, they have been used to assign special truth values to atoms which possess certain computational behaviour such as being nonterminating ( 11, 20] being ill typed ( 21] being floundering ([4]) or failing when backtracking ( 6] The motivation for the definitions of the three valued logics we will be using in this paper comes from a couple of sources. Primarily, these logics are formulated in order to allow for easy analysis and characterization of the programs or classes of programs ....

.... Phi P;3 The second three valued logic, L 2 , will be used for studying acceptable programs and is non commutative under conjunction. It will be sufficient to evaluate u f to u instead of f and leaving the truth table for L 1 otherwise unchanged. This way of defining conjunction was employed in [4] and [6] see also the discussion of LISP in [13] The truth table is again given in Table 1. The third logic, L 3 , will be used for studying locally hierarchical and acyclic programs. For this purpose, we use a commutative version of L 2 where we evaluate f u to u instead of f, see the ....

Andrews, J.H.: A Logical Semantics for Depth-first Prolog with Ground Negation. Theoretical Computer Science 184 (1--2) (1997) 105--143

....rightward extension and rightward contraction. Also, incorporation of negation on goals was proposed by the use of a second sequent implication ) Gamma . 12.3 Andrews An operational semantics for Prolog, including negation as failure and floundering on non ground negative goals, is given in [3]. The operational semantics is based on the Clark completion of programs, and has the form of a derivational calculus. The semantics is sound and complete with respect to a truthfunctional semantics in the form of a valuation function. This valuation function, defined for the class of ....

J.H. Andrews, A logical semantics for depth-first Prolog with ground negation, Proceedings ICLP, Vancouver, Canada, 1993.

....by virtue of its logical soundness; accordingly, SLD resolution also has the least model semantics. As another example, Prolog programming with unsound negation as failure does not have the witness properties (for instance, x = 0) fails even though : 1 = 0) succeeds) but both Andrews [And97] and Stark [Sta98] have identified restricted operational models of Prolog with sound negation as failure, which regain the witness properties and also permit abstract, non reifying semantics. More recently Elbl [Elb99] has produced abstract compositional semantics for such systems. The Andrews, ....

....it equivalent to the conservative operational semantics. The witness properties are important to the abstract semantics, and are in fact used formally in the proof of equivalence. The abstract semantics is very similar to Andrews abstract semantics of logic programming with negation as failure [And97] In Section 10, we apply this abstract semantics by deriving various useful rules for proving properties of programs, and using those properties in a specific proof. Finally, in Section 11 we give some conclusions and suggestions for further research. 2 Background and Related Work In this ....

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James H. Andrews. A logical semantics for depth-first Prolog with ground negation. Theoretical Computer Science, 184(1-2):105--143, September 1997.

....of Prolog goals not involving reified answer substitutions and unification. That characterization takes account only of depthfirst Prolog without builtins, negation or cut. We then adapted this characterization to a true abstract semantics, which also takes into account ground negation as failure [And93, And97] Stark characterized a similar subset of Prolog, with the addition of builtins but with a mode restriction [Sta94, Sta98] he also showed that a system to help users prove properties of programs can be built on such a characterization. More recently, Elbl [Elb99] has given a semantics for ....

James H. Andrews. A logical semantics for depth-first Prolog with ground negation. In Proceedings of the International Logic Programming Symposium, Vancouver, October 1993. MIT Press.

....of other forms of practical negation, or of other language features involving groundness conditions. This material was published earlier as a technical report [And93a] and is the expanded version, including proofs, of a paper presented at the 1993 International Logic Programming Symposium (ILPS) [And93b]. Keywords: Logical extensions, Semantic analysis, Negation. 1 Introduction Sometimes it is possible to take a seemingly non logical feature of a logic programming system, and give it a more logical interpretation by extending our traditional notions of semantics. In [And90, And91] it was ....

....in their work, thus going beyond the scope of this paper. They are also exploring practical methods for proving termination, which I have not attempted to touch on. Recently, Stark [Sta94] has published a semantics for depth first Prolog with negation which covers some of the same ground as [And93b]. Stark s method is to translate a Prolog program into a new program in which each predicate is translated into three predicates: one corresponding to success, one corresponding to failure, and one corresponding to lefttermination of the original predicate. However, Stark avoids the problem of ....

James H. Andrews. A logical semantics for depth-first Prolog with ground negation. In Proceedings of the International Logic Programming Symposium, Vancouver, October 1993. MIT Press.

....provides the semantics with a logical analogue of free variables. This intriguing technique may open the door to the characterization of other forms of practical negation, or of other language features involving groundness conditions. This material was published earlier as a technical report [And93a] and is the expanded version, including proofs, of a paper presented at the 1993 International Logic Programming Symposium (ILPS) And93b] Keywords: Logical extensions, Semantic analysis, Negation. 1 Introduction Sometimes it is possible to take a seemingly non logical feature of a logic ....

James H. Andrews. A logical semantics for depth-first Prolog with ground negation. Technical Report 93-10, Centre for Systems Science, Simon Fraser University, Burnaby, British Columbia, Canada, 1993.

....Implementation: SVP It is perhaps easiest to introduce the spreadsheet presentation by describing an actual implementation. The proof assistant SVP is a system for proving properties of Prolog programs, based on the author s semantics for depth first, left toright Prolog with ground negation [And91, And93, And97]. It uses a scrolling, ASCII command loop interface. At every command which changes the state of Stage 5, proof of s list(X) s append(X, X) Sequent Fml# Formula a b c d ....

James H. Andrews. A logical semantics for depth-first Prolog with ground negation. Theoretical Computer Science, 184(1-2):105--143, September 1997.

....Implementation: SVP It is perhaps easiest to introduce the spreadsheet presentation by describing an actual implementation. The proof assistant SVP is a system for proving properties of Prolog programs, based on the author s semantics for depth first, left toright Prolog with ground negation [And91, And93, And97]. It uses a scrolling, ASCII command loop interface. At every command which changes the state of Stage 5, proof of s list(X) s append(X, X) Sequent Fml# Formula a b c d ....

James H. Andrews. A logical semantics for depth-first Prolog with ground negation. In Proceedings of the International Logic Programming Symposium, Vancouver, October 1993. MIT Press.

....in the axiomatization, for instance to tell when a condition is not satisfied. Lambda Prolog implements negation as failure (NAF) Cla78] In general, the form of NAF it uses is unsafe, in that it can return invalid results; but it is safe if no uninstantiated variables are used within negations [And93, Sta94]. We claim that for step sequence queries such as those above, this condition is always satisfied. Thus we can compute the outcome of a state given an event script; but we cannot, for instance, run a query of the form (step sequence State Script Final state Trace) where Script is not instantiated ....

James H. Andrews. A logical semantics for depth-first Prolog with ground negation. In Proceedings of the International Logic Programming Symposium, Vancouver, October 1993. MIT Press.

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