Indexed Categories and Bottom-Up Semantics of Logic Programs

2001 ◽  
pp. 438-454 ◽  
Author(s):  
Gianluca Amato ◽  
James Lipton
Keyword(s):  
Logic Programs ◽  
Bottom Up ◽  
Indexed Categories ◽  
Semantics Of Logic Programs

scholarly journals Checking termination of bottom-up evaluation of logic programs with function symbols

2014 ◽  
Vol 15 (6) ◽  
pp. 854-889 ◽  
Author(s):  
MARCO CALAUTTI ◽  
SERGIO GRECO ◽  
FRANCESCA SPEZZANO ◽  
IRINA TRUBITSYNA
Keyword(s):  
Evaluation Procedure ◽  
Extended Version ◽  
Logic Programs ◽  
Safety Criterion ◽  
Bottom Up ◽  
Program Termination ◽  
Termination Criteria ◽  
Safety Function ◽  
Semantics Of Logic Programs ◽  
Termination Problem

AbstractRecently, there has been an increasing interest in the bottom-up evaluation of the semantics of logic programs with complex terms. The presence of function symbols in the program may render the ground instantiation infinite, and finiteness of models and termination of the evaluation procedure, in the general case, are not guaranteed anymore. Since the program termination problem is undecidable in the general case, several decidable criteria (called program termination criteria) have been recently proposed. However, current conditions are not able to identify even simple programs, whose bottom-up execution always terminates. The paper introduces new decidable criteria for checking termination of logic programs with function symbols under bottom-up evaluation, by deeply analyzing the program structure. First, we analyze the propagation of complex terms among arguments by means of the extended version of the argument graph calledpropagation graph. The resulting criterion, calledacyclicity, generalizes most of the decidable criteria proposed so far. Next, we study how rules may activate each other and define a more powerful criterion, calledsafety. This criterion uses the so-calledsafety functionable to analyze how rules may activate each other and how the presence of some arguments in a rule limits its activation. We also study the application of the proposed criteria to bound queries and show that the safety criterion is well-suited to identify relevant classes of programs and bound queries. Finally, we propose a hierarchy of classes of terminating programs, calledk-safety, where thek-safe class strictly includes the (k-1)-safe class.

scholarly journals Complete Bottom-Up Predicate Invention in Meta-Interpretive Learning

2020 ◽  
Author(s):  
Céline Hocquette ◽  
Stephen H. Muggleton
Keyword(s):  
State Of The Art ◽  
Order Logic ◽  
Learning Performance ◽  
Sample Complexity ◽  
Logic Programs ◽  
Top Down ◽  
Bottom Up ◽  
Predicate Invention ◽  
Feature Discovery ◽  
Second Order Logic

Predicate Invention in Meta-Interpretive Learning (MIL) is generally based on a top-down approach, and the search for a consistent hypothesis is carried out starting from the positive examples as goals. We consider augmenting top-down MIL systems with a bottom-up step during which the background knowledge is generalised with an extension of the immediate consequence operator for second-order logic programs. This new method provides a way to perform extensive predicate invention useful for feature discovery. We demonstrate this method is complete with respect to a fragment of dyadic datalog. We theoretically prove this method reduces the number of clauses to be learned for the top-down learner, which in turn can reduce the sample complexity. We formalise an equivalence relation for predicates which is used to eliminate redundant predicates. Our experimental results suggest pairing the state-of-the-art MIL system Metagol with an initial bottom-up step can significantly improve learning performance.

scholarly journals Bottom-up abstract interpretation of logic programs

1994 ◽  
Vol 124 (1) ◽  
pp. 93-125 ◽  
Author(s):  
Michael Codish ◽  
Dennis Dams ◽  
Eyal Yardeni
Keyword(s):  
Abstract Interpretation ◽  
Logic Programs ◽  
Bottom Up

TOPOLOGY AND THE SEMANTICS OF LOGIC PROGRAMS

1995 ◽  
Vol 24 (4) ◽  
pp. 359-386 ◽  
Author(s):  
Anthony Karel Seda
Keyword(s):  
Logic Programs ◽  
Semantics Of Logic Programs

scholarly journals Well-founded and stable semantics of logic programs with aggregates

2007 ◽  
Vol 7 (3) ◽  
pp. 301-353 ◽  
Author(s):  
NIKOLAY PELOV ◽  
MARC DENECKER ◽  
MAURICE BRUYNOOGHE
Keyword(s):  
Logic Programming ◽  
Second Order ◽  
Logic Programs ◽  
Consequence Operator ◽  
Trade Offs ◽  
Stable Semantics ◽  
Consequence Operators ◽  
Semantics Of Logic Programs ◽  
Stable Models

AbstractIn this paper, we present a framework for the semantics and the computation of aggregates in the context of logic programming. In our study, an aggregate can be an arbitrary interpreted second order predicate or function. We define extensions of the Kripke-Kleene, the well-founded and the stable semantics for aggregate programs. The semantics is based on the concept of a three-valuedimmediate consequence operatorof an aggregate program. Such an operatorapproximatesthe standard two-valued immediate consequence operator of the program, and induces a unique Kripke-Kleene model, a unique well-founded model and a collection of stable models. We study different ways of defining such operators and thus obtain a framework of semantics, offering different trade-offs betweenprecisionandtractability. In particular, we investigate conditions on the operator that guarantee that the computation of the three types of semantics remains on the same level as for logic programs without aggregates. Other results show that, in practice, even efficient three-valued immediate consequence operators which are very low in the precision hierarchy, still provide optimal precision.

scholarly journals Compiling bottom-up and mixed derivations into top-down executable logic programs

1991 ◽  
Vol 7 (3) ◽  
pp. 337-358 ◽  
Author(s):  
Danny De Schreye ◽  
Bern Martens ◽  
Gunther Sablon ◽  
Maurice Bruynooghe
Keyword(s):  
Logic Programs ◽  
Top Down ◽  
Bottom Up
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