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

Efficient bottom-up execution of logic programs using abstract interpretation

1993 ◽  
Vol 47 (3) ◽  
pp. 149-157
Author(s):  
Byeong-Mo Chang ◽  
Kwang-Moo Choe ◽  
Taisook Han
Keyword(s):  
Abstract Interpretation ◽  
Logic Programs ◽  
Bottom Up

scholarly journals An effective fixpoint semantics for linear logic programs

2001 ◽  
Vol 2 (1) ◽  
pp. 85-122 ◽  
Author(s):  
MARCO BOZZANO ◽  
GIORGIO DELZANNO ◽  
MAURIZIO MARTELLI
Keyword(s):  
Logic Programming ◽  
Petri Nets ◽  
Abstract Interpretation ◽  
Theoretical Foundation ◽  
Linear Logic ◽  
Sufficient Conditions ◽  
Logic Programs ◽  
Bottom Up ◽  
Interesting Class ◽  
Fixpoint Semantics

In this paper we investigate the theoretical foundation of a new bottom-up semantics for linear logic programs, and more precisely for the fragment of LinLog (Andreoli, 1992) that consists of the language LO (Andreoli & Pareschi, 1991) enriched with the constant 1. We use constraints to symbolically and finitely represent possibly infinite collections of provable goals. We define a fixpoint semantics based on a new operator in the style of TP working over constraints. An application of the fixpoint operator can be computed algorithmically. As sufficient conditions for termination, we show that the fixpoint computation is guaranteed to converge for propositional LO. To our knowledge, this is the first attempt to define an effective fixpoint semantics for linear logic programs. As an application of our framework, we also present a formal investigation of the relations between LO and Disjunctive Logic Programming (Minker et al., 1991). Using an approach based on abstract interpretation, we show that DLP fixpoint semantics can be viewed as an abstraction of our semantics for LO. We prove that the resulting abstraction is correct and complete (Cousot & Cousot, 1977; Giacobazzi & Ranzato, 1997) for an interesting class of LO programs encoding Petri Nets.

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.

Improving Execution Models of Logic Programs by Two-phase Abstract Interpretation

ETRI Journal ◽  
1995 ◽  
Vol 16 (4) ◽  
pp. 27-47
Author(s):  
Byeong-Mo Chang Chang ◽  
Kwang-Moo Choe Choe ◽  
Roberto Giacobazzi Giacobazzi
Keyword(s):  
Abstract Interpretation ◽  
Logic Programs ◽  
Two Phase ◽  
Execution Models

scholarly journals A backward analysis for constraint logic programs

2002 ◽  
Vol 2 (4-5) ◽  
pp. 517-547 ◽  
Author(s):  
ANDY KING ◽  
LUNJIN LU
Keyword(s):  
Ad Hoc ◽  
Abstract Interpretation ◽  
Logic Program ◽  
Control Flow ◽  
Third Party ◽  
Logic Programs ◽  
Abstract Domains ◽  
Constraint Logic Programs ◽  
Backward Analysis ◽  
Computational Properties

One recurring problem in program development is that of understanding how to re-use code developed by a third party. In the context of (constraint) logic programming, part of this problem reduces to figuring out how to query a program. If the logic program does not come with any documentation, then the programmer is forced to either experiment with queries in an ad hoc fashion or trace the control-flow of the program (backward) to infer the modes in which a predicate must be called so as to avoid an instantiation error. This paper presents an abstract interpretation scheme that automates the latter technique. The analysis presented in this paper can infer moding properties which if satisfied by the initial query, come with the guarantee that the program and query can never generate any moding or instantiation errors. Other applications of the analysis are discussed. The paper explains how abstract domains with certain computational properties (they condense) can be used to trace control-flow backward (right-to-left) to infer useful properties of initial queries. A correctness argument is presented and an implementation is reported.

Sign in / Sign up

Export Citation Format

Share Document