Unfold/fold transformations of logic programs

1992 ◽  
Vol 2 (2) ◽  
pp. 143-157 ◽  
Author(s):  
J. C. Shepherdson
Keyword(s):  
Logic Programming ◽  
Recent Work ◽  
Logic Programs ◽  
Declarative Semantics ◽  
Model Completion

Unfold/fold transformations have been used in logic programming for some years to transform programs into more efficient ones. We describe recent work on the extent to which these transformations produce programs which are equivalent to the original one. Various notions of equivalence are considered: same success set; finite failure set; least Herbrand model; completion. This is used to illustrate the rather unsatisfactory relationship between logic programming and logic shown by the wide variety of different declarative semantics proposed for logic programs.

scholarly journals Fuzzy linguistic logic programming and its applications

2009 ◽  
Vol 9 (3) ◽  
pp. 309-341 ◽  
Author(s):  
VAN HUNG LE ◽  
FEI LIU ◽  
DINH KHANG TRAN
Keyword(s):  
Logic Programming ◽  
Logic Programs ◽  
Linguistic Terms ◽  
Natural Languages ◽  
Procedural Semantics ◽  
Declarative Semantics ◽  
Linguistic Hedges ◽  
Fuzzy Linguistic ◽  
Semantics Of Logic Programs ◽  
Different Levels

AbstractThe paper introduces fuzzy linguistic logic programming, which is a combination of fuzzy logic programming, introduced by P. Vojtáš, and hedge algebras in order to facilitate the representation and reasoning on human knowledge expressed in natural languages. In fuzzy linguistic logic programming, truth values are linguistic ones, e.g., VeryTrue, VeryProbablyTrue and LittleFalse, taken from a hedge algebra of a linguistic truth variable, and linguistic hedges (modifiers) can be used as unary connectives in formulae. This is motivated by the fact that humans reason mostly in terms of linguistic terms rather than in terms of numbers, and linguistic hedges are often used in natural languages to express different levels of emphasis. The paper presents: (a) the language of fuzzy linguistic logic programming; (b) a declarative semantics in terms of Herbrand interpretations and models; (c) a procedural semantics which directly manipulates linguistic terms to compute a lower bound to the truth value of a query, and proves its soundness; (d) a fixpoint semantics of logic programs, and based on it, proves the completeness of the procedural semantics; (e) several applications of fuzzy linguistic logic programming; and (f) an idea of implementing a system to execute fuzzy linguistic logic programs.

A Modal Semantics of Negation in Logic Programming

1992 ◽  
Vol 16 (3-4) ◽  
pp. 231-262
Author(s):  
Philippe Balbiani
Keyword(s):  
Modal Logic ◽  
Logic Programming ◽  
Modal Logics ◽  
Kripke Models ◽  
Logic Programs ◽  
Modal Semantics ◽  
Soundness And Completeness ◽  
Modal Completion ◽  
Well Foundedness

The beauty of modal logics and their interest lie in their ability to represent such different intensional concepts as knowledge, time, obligation, provability in arithmetic, … according to the properties satisfied by the accessibility relations of their Kripke models (transitivity, reflexivity, symmetry, well-foundedness, …). The purpose of this paper is to study the ability of modal logics to represent the concepts of provability and unprovability in logic programming. The use of modal logic to study the semantics of logic programming with negation is defended with the help of a modal completion formula. This formula is a modal translation of Clack’s formula. It gives soundness and completeness proofs for the negation as failure rule. It offers a formal characterization of unprovability in logic programs. It characterizes as well its stratified semantics.

scholarly journals Learning Large Logic Programs By Going Beyond Entailment

2020 ◽  
Author(s):  
Andrew Cropper ◽  
Sebastijan Dumančic
Keyword(s):  
Logic Programming ◽  
Loss Function ◽  
Inductive Logic Programming ◽  
State Of The Art ◽  
Inductive Logic ◽  
Program Synthesis ◽  
Loss Functions ◽  
Logic Programs ◽  
Binary Decision ◽  
Best First Search

A major challenge in inductive logic programming (ILP) is learning large programs. We argue that a key limitation of existing systems is that they use entailment to guide the hypothesis search. This approach is limited because entailment is a binary decision: a hypothesis either entails an example or does not, and there is no intermediate position. To address this limitation, we go beyond entailment and use 'example-dependent' loss functions to guide the search, where a hypothesis can partially cover an example. We implement our idea in Brute, a new ILP system which uses best-first search, guided by an example-dependent loss function, to incrementally build programs. Our experiments on three diverse program synthesis domains (robot planning, string transformations, and ASCII art), show that Brute can substantially outperform existing ILP systems, both in terms of predictive accuracies and learning times, and can learn programs 20 times larger than state-of-the-art systems.

scholarly journals onlineSPARC: A Programming Environment for Answer Set Programming

2018 ◽  
Vol 19 (2) ◽  
pp. 262-289 ◽  
Author(s):  
ELIAS MARCOPOULOS ◽  
YUANLIN ZHANG
Keyword(s):  
High School Students ◽  
Logic Programming ◽  
Answer Set Programming ◽  
Programming Environment ◽  
Logic Programs ◽  
School Students ◽  
Major Barrier ◽  
Simple Interface ◽  
Answer Sets ◽  
Answer Set

AbstractRecent progress in logic programming (e.g. the development of the answer set programming (ASP) paradigm) has made it possible to teach it to general undergraduate and even middle/high school students. Given the limited exposure of these students to computer science, the complexity of downloading, installing, and using tools for writing logic programs could be a major barrier for logic programming to reach a much wider audience. We developed onlineSPARC, an online ASP environment with a self-contained file system and a simple interface. It allows users to type/edit logic programs and perform several tasks over programs, including asking a query to a program, getting the answer sets of a program, and producing a drawing/animation based on the answer sets of a program.

scholarly journals Induction of Non-Monotonic Logic Programs to Explain Boosted Tree Models Using LIME

2019 ◽  
Vol 33 ◽  
pp. 3052-3059 ◽  
Author(s):  
Farhad Shakerin ◽  
Gopal Gupta
Keyword(s):  
Logic Programming ◽  
Inductive Logic Programming ◽  
State Of The Art ◽  
Inductive Logic ◽  
Nonmonotonic Logic ◽  
Global Behavior ◽  
Logic Programs ◽  
Tree Models ◽  
Boosted Tree ◽  
Classification Evaluation

We present a heuristic based algorithm to induce nonmonotonic logic programs that will explain the behavior of XGBoost trained classifiers. We use the technique based on the LIME approach to locally select the most important features contributing to the classification decision. Then, in order to explain the model’s global behavior, we propose the LIME-FOLD algorithm —a heuristic-based inductive logic programming (ILP) algorithm capable of learning nonmonotonic logic programs—that we apply to a transformed dataset produced by LIME. Our proposed approach is agnostic to the choice of the ILP algorithm. Our experiments with UCI standard benchmarks suggest a significant improvement in terms of classification evaluation metrics. Meanwhile, the number of induced rules dramatically decreases compared to ALEPH, a state-of-the-art ILP system.

scholarly journals Products of weighted logic programs

2011 ◽  
Vol 11 (2-3) ◽  
pp. 263-296 ◽  
Author(s):  
SHAY B. COHEN ◽  
ROBERT J. SIMMONS ◽  
NOAH A. SMITH
Keyword(s):  
Machine Learning ◽  
Dynamic Programming ◽  
Logic Programming ◽  
Scoring Function ◽  
Logic Programs ◽  
Information Theoretic ◽  
Optimal Score ◽  
Leibler Divergence ◽  
Programming Algorithms ◽  
Output Space

AbstractWeighted logic programming, a generalization of bottom-up logic programming, is a well-suited framework for specifying dynamic programming algorithms. In this setting, proofs correspond to the algorithm's output space, such as a path through a graph or a grammatical derivation, and are given a real-valued score (often interpreted as a probability) that depends on the real weights of the base axioms used in the proof. The desired output is a function over all possible proofs, such as a sum of scores or an optimal score. We describe the product transformation, which can merge two weighted logic programs into a new one. The resulting program optimizes a product of proof scores from the original programs, constituting a scoring function known in machine learning as a “product of experts.” Through the addition of intuitive constraining side conditions, we show that several important dynamic programming algorithms can be derived by applying product to weighted logic programs corresponding to simpler weighted logic programs. In addition, we show how the computation of Kullback–Leibler divergence, an information-theoretic measure, can be interpreted using product.

scholarly journals Interdefinability of defeasible logic and logic programming under the well-founded semantics

2011 ◽  
Vol 13 (1) ◽  
pp. 107-142 ◽  
Author(s):  
FREDERICK MAIER
Keyword(s):  
Logic Programming ◽  
Opposite Direction ◽  
Stable Model ◽  
Logic Programs ◽  
Defeasible Logic ◽  
Normal Logic

AbstractWe provide a method of translating theories of Nute's defeasible logic into logic programs, and a corresponding translation in the opposite direction. Under certain natural restrictions, the conclusions of defeasible theories under the ambiguity propagating defeasible logic ADL correspond to those of the well-founded semantics for normal logic programs, and so it turns out that the two formalisms are closely related. Using the same translation of logic programs into defeasible theories, the semantics for the ambiguity blocking defeasible logic NDL can be seen as indirectly providing an ambiguity blocking semantics for logic programs. We also provide antimonotone operators for both ADL and NDL, each based on the Gelfond–Lifschitz (GL) operator for logic programs. For defeasible theories without defeaters or priorities on rules, the operator for ADL corresponds to the GL operator and so can be seen as partially capturing the consequences according to ADL. Similarly, the operator for NDL captures the consequences according to NDL, though in this case no restrictions on theories apply. Both operators can be used to define stable model semantics for defeasible theories.

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 Productive corecursion in logic programming

2017 ◽  
Vol 17 (5-6) ◽  
pp. 906-923 ◽  
Author(s):  
EKATERINA KOMENDANTSKAYA ◽  
YUE LI
Keyword(s):  
Data Structure ◽  
Logic Programming ◽  
State Of The Art ◽  
Logic Program ◽  
Stream Processing ◽  
The Internet ◽  
Logic Programs ◽  
Algorithmic Solution ◽  
Undecidable Property ◽  
Turing Complete

AbstractLogic Programming is a Turing complete language. As a consequence, designing algorithms that decide termination and non-termination of programs or decide inductive/coinductive soundness of formulae is a challenging task. For example, the existing state-of-the-art algorithms can only semi-decide coinductive soundness of queries in logic programming for regular formulae. Another, less famous, but equally fundamental and important undecidable property is productivity. If a derivation is infinite and coinductively sound, we may ask whether the computed answer it determines actually computes an infinite formula. If it does, the infinite computation is productive. This intuition was first expressed under the name of computations at infinity in the 80s. In modern days of the Internet and stream processing, its importance lies in connection to infinite data structure processing. Recently, an algorithm was presented that semi-decides a weaker property – of productivity of logic programs. A logic program is productive if it can give rise to productive derivations. In this paper, we strengthen these recent results. We propose a method that semi-decides productivity of individual derivations for regular formulae. Thus, we at last give an algorithmic counterpart to the notion of productivity of derivations in logic programming. This is the first algorithmic solution to the problem since it was raised more than 30 years ago. We also present an implementation of this algorithm.

Constraint logic programming

1991 ◽  
Vol 6 (3) ◽  
pp. 151-194 ◽  
Author(s):  
Pascal Van Hentenryck
Keyword(s):  
Logic Programming ◽  
Programming Languages ◽  
Constraint Logic Programming ◽  
Combinatorial Problems ◽  
Basic Operation ◽  
Combinatorial Search ◽  
New Class ◽  
Constraint Systems ◽  
Declarative Semantics ◽  
Relational Form

AbstractConstraint logic programming (CLP) is a generalization of logic programming (LP) where unification, the basic operation of LP languages, is replaced by constraint handling in a constraint system. The resulting languages combine the advantages of LP (declarative semantics, nondeterminism, relational form) with the efficiency of constraint-solving algorithms. For some classes of combinatorial search problems, they shorten the development time significantly while preserving most of the efficiency of imperative languages. This paper surveys this new class of programming languages from their underlying theory, to their constraint systems, and to their applications to combinatorial problems.

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