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.

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 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 Termination prediction for general logic programs

2009 ◽  
Vol 9 (6) ◽  
pp. 751-780 ◽  
Author(s):  
YI-DONG SHEN ◽  
DANNY DE SCHREYE ◽  
DEAN VOETS
Keyword(s):  
State Of The Art ◽  
Logic Program ◽  
Time Limit ◽  
Experimental Results ◽  
Prediction Tool ◽  
Logic Programs ◽  
General Logic ◽  
Necessary And Sufficient ◽  
Termination Problem

AbstractWe present a heuristic framework for attacking the undecidable termination problem of logic programs, as an alternative to current termination/nontermination proof approaches. We introduce an idea of termination prediction, which predicts termination of a logic program in case that neither a termination nor a non-termination proof is applicable. We establish a necessary and sufficient characterization of infinite (generalized) SLDNF-derivations with arbitrary (concrete or moded) queries, and develop an algorithm that predicts termination of general logic programs with arbitrary nonfloundering queries. We have implemented a termination prediction tool and obtained quite satisfactory experimental results. Except for five programs which break the experiment time limit, our prediction is 100% correct for all 296 benchmark programs of the Termination Competition 2007, of which 18 programs cannot be proved by any of the existing state-of-the-art analyzers like AProVE07, NTI, Polytool, and TALP.

scholarly journals Optimizing Answer Set Computation via Heuristic-Based Decomposition

2019 ◽  
Vol 19 (04) ◽  
pp. 603-628 ◽  
Author(s):  
FRANCESCO CALIMERI ◽  
SIMONA PERRI ◽  
JESSICA ZANGARI
Keyword(s):  
Logic Programming ◽  
Logic Program ◽  
Answer Set Programming ◽  
Decomposition Techniques ◽  
Logic Programs ◽  
Experimental Activity ◽  
Performance Of Systems ◽  
Answer Sets ◽  
The Impact ◽  
Answer Set

AbstractAnswer Set Programming (ASP) is a purely declarative formalism developed in the field of logic programming and non-monotonic reasoning: computational problems are encoded by logic programs whose answer sets, corresponding to solutions, are computed by an ASP system. Different, semantically equivalent, programs can be defined for the same problem; however, performance of systems evaluating them might significantly vary. We propose an approach for automatically transforming an input logic program into an equivalent one that can be evaluated more efficiently. One can make use of existing tree-decomposition techniques for rewriting selected rules into a set of multiple ones; the idea is to guide and adaptively apply them on the basis of proper new heuristics, to obtain a smart rewriting algorithm to be integrated into an ASP system. The method is rather general: it can be adapted to any system and implement different preference policies. Furthermore, we define a set of new heuristics tailored at optimizing grounding, one of the main phases of the ASP computation; we use them in order to implement the approach into the ASP systemDLV, in particular into its grounding subsystemℐ-DLV, and carry out an extensive experimental activity for assessing the impact of the proposal.

scholarly journals Programming in logic without logic programming

2016 ◽  
Vol 16 (3) ◽  
pp. 269-295 ◽  
Author(s):  
ROBERT KOWALSKI ◽  
FARIBA SADRI
Keyword(s):  
Logic Programming ◽  
Logic Program ◽  
Operational Semantics ◽  
Canonical Model ◽  
State Transitions ◽  
Logic Programs ◽  
Initial State ◽  
State Sequence ◽  
Sequence Of Events ◽  
Current State

AbstractIn previous work, we proposed a logic-based framework in which computation is the execution of actions in an attempt to make reactive rules of the form if antecedent then consequent true in a canonical model of a logic program determined by an initial state, sequence of events, and the resulting sequence of subsequent states. In this model-theoretic semantics, reactive rules are the driving force, and logic programs play only a supporting role. In the canonical model, states, actions, and other events are represented with timestamps. But in the operational semantics (OS), for the sake of efficiency, timestamps are omitted and only the current state is maintained. State transitions are performed reactively by executing actions to make the consequents of rules true whenever the antecedents become true. This OS is sound, but incomplete. It cannot make reactive rules true by preventing their antecedents from becoming true, or by proactively making their consequents true before their antecedents become true. In this paper, we characterize the notion of reactive model, and prove that the OS can generate all and only such models. In order to focus on the main issues, we omit the logic programming component of the framework.

ON A THEOREM PROVER FOR VARIATIONAL LOGIC PROGRAMS WITH FUNCTORS SETU AND SETS

2000 ◽  
Vol 08 (01) ◽  
pp. 73-92 ◽  
Author(s):  
HIROSHI SAKAI ◽  
AKIMICHI OKUMA
Keyword(s):  
Logic Programming ◽  
Soft Computing ◽  
Logic Program ◽  
Theorem Prover ◽  
Logic Programs

We are now touching a problem how we add soft computing aspects to logic programming and we have been discussing null attribute values on logic programs. Here, we introduce two functors setu and sets into logic programs for describing indefinite attribute values explicitly. Every logic program with setu or sets has variability and tolerance in itself, namely this program expresses a set of possible definite logic programs. We call this program a variational logic program. In this paper, we show the variational logic programs and a theorem prover for them.

scholarly journals On the Semantics of Logic Programs with Preferences

2007 ◽  
Vol 30 ◽  
pp. 501-523 ◽  
Author(s):  
S. Greco ◽  
I. Trubitsyna ◽  
E. Zumpano
Keyword(s):  
Logic Programming ◽  
Complexity Analysis ◽  
Structural Information ◽  
Logic Program ◽  
Set Optimization ◽  
Logic Programs ◽  
Preference Relations ◽  
New Interpretation ◽  
Semantics Of Logic Programs ◽  
Stable Models

This work is a contribution to prioritized reasoning in logic programming in the presence of preference relations involving atoms. The technique, providing a new interpretation for prioritized logic programs, is inspired by the semantics of Prioritized Logic Programming and enriched with the use of structural information of preference of Answer Set Optimization Programming. Specifically, the analysis of the logic program is carried out together with the analysis of preferences in order to determine the choice order and the sets of comparable models. The new semantics is compared with other approaches known in the literature and complexity analysis is also performed, showing that, with respect to other similar approaches previously proposed, the complexity of computing preferred stable models does not increase.

DEFINITION AND ADAPTATION OF WEIGHTED FUZZY LOGIC PROGRAMS

2009 ◽  
Vol 17 (01) ◽  
pp. 85-135 ◽  
Author(s):  
ALEXANDROS CHORTARAS ◽  
GIORGOS STAMOU ◽  
ANDREAS STAFYLOPATIS
Keyword(s):  
Fuzzy Logic ◽  
Logic Programming ◽  
General Framework ◽  
Logic Program ◽  
Logic Programs ◽  
Truth Value ◽  
The Individual ◽  
Logic Rule

Fuzzy logic programming has been lately used as a general framework for representing and handling imprecise knowledge. In this paper, we define the syntax and the semantics of definite weighted fuzzy logic programs, which extend definite fuzzy logic programs by allowing the inclusion of different significance weights in the individual atoms that make up the antecedent of a fuzzy logic rule. The weights add expressiveness to a fuzzy logic program and allow the determination of the level up to which an atom in the antecedent of a rule may affect the truth value of its consequent. In describing the semantics of definite weighted fuzzy logic programs we introduce the notion of the generalized weighted fuzzy conjunction operator, which can be regarded as a weighted t-norm based aggregation. We determine the properties of generalized weighted fuzzy conjunction operators and provide several examples. A methodology for constructing generalized weighted fuzzy conjunction operators using generator functions of existing t-norms is also introduced. Finally, a method for setting up a parametric weighted fuzzy logic program and automatically adapting the weights of its rules using a numerical dataset is developed.

scholarly journals Semantics for Possibilistic Disjunctive Programs

2011 ◽  
Vol 13 (1) ◽  
pp. 33-70 ◽  
Author(s):  
JUAN CARLOS NIEVES ◽  
MAURICIO OSORIO ◽  
ULISES CORTÉS
Keyword(s):  
Logic Programming ◽  
Knowledge Base ◽  
Logic Program ◽  
Programming Approach ◽  
Logic Programs ◽  
Possibilistic Logic ◽  
Point Operator ◽  
Disjunctive Logic Programs ◽  
Answer Sets ◽  
Disjunctive Programs

AbstractIn this paper, a possibilistic disjunctive logic programming approach for modeling uncertain, incomplete, and inconsistent information is defined. This approach introduces the use of possibilistic disjunctive clauses, which are able to capture incomplete information and states of a knowledge base at the same time. By considering a possibilistic logic program as a possibilistic logic theory, a construction of a possibilistic logic programming semantic based on answer sets and the proof theory of possibilistic logic is defined. It shows that this possibilistic semantics for disjunctive logic programs can be characterized by a fixed-point operator. It is also shown that the suggested possibilistic semantics can be computed by a resolution algorithm and the consideration of optimal refutations from a possibilistic logic theory. In order to manage inconsistent possibilistic logic programs, a preference criterion between inconsistent possibilistic models is defined. In addition, the approach of cuts for restoring consistency of an inconsistent possibilistic knowledge base is adopted. The approach is illustrated in a medical scenario.

The language of epistemic specifications (refined) including a prototype solver

2015 ◽  
Vol 30 (4) ◽  
pp. 953-989 ◽  
Author(s):  
Patrick Kahl ◽  
Richard Watson ◽  
Evgenii Balai ◽  
Michael Gelfond ◽  
Yuanlin Zhang
Keyword(s):  
Logic Programming ◽  
Programming Language ◽  
Epistemic Logic ◽  
Formal Semantics ◽  
Logic Program ◽  
Logic Programs ◽  
Logic Programming Language ◽  
Conformant Planning

Abstract In this article, we present a new version of the language of Epistemic Specifications. The goal is to simplify and improve the intuitive and formal semantics of the language. We describe an algorithm for computing solutions of programs written in this new version of the language. The new semantics is illustrated by a number of examples, including an Epistemic Specifications-based framework for conformant planning. In addition, we introduce the notion of an epistemic logic program with sorts . This extends recent efforts to define a logic programming language that includes the means for explicitly specifying the domains of predicate parameters. An algorithm and its implementation as a solver for epistemic logic programs with sorts is also discussed.

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