scholarly journals First-Order Modular Logic Programs and their Conservative Extensions (Extended Abstract)

2017 ◽  
Author(s):  
Amelia Harrison ◽  
Yuliya Lierler
Keyword(s):  
Logic Programming ◽  
Short Version ◽  
Logic Programs ◽  
Conservative Extension ◽  
International Conference ◽  
First Order ◽  
Modular Logic ◽  
Traditional Programs ◽  
The Common ◽  
Conservative Extensions

This paper introduces first-order modular logic programs, which provide a way of viewing answer set programs as consisting of many independent, meaningful modules. We also present conservative extensions of such programs. This concept helps to identify strong relationships between modular programs as well as between traditional programs. For example, we illustrate how the notion of a conservative extension can be used to justify the common projection rewriting. This is a short version of a paper was presented at the 32nd International Conference on Logic Programming (Harrison and Lierler, 2016).

scholarly journals First-order modular logic programs and their conservative extensions

2016 ◽  
Vol 16 (5-6) ◽  
pp. 755-770 ◽  
Author(s):  
AMELIA HARRISON ◽  
YULIYA LIERLER
Keyword(s):  
Logic Programs ◽  
Conservative Extension ◽  
First Order ◽  
Modular Logic ◽  
Traditional Programs ◽  
The Common ◽  
Conservative Extensions ◽  
Answer Set ◽  
Strong Relationships

AbstractModular logic programs provide a way of viewing logic programs as consisting of many independent, meaningful modules. This paper introduces first-order modular logic programs, which can capture the meaning of many answer set programs. We also introduce conservative extensions of such programs. This concept helps to identify strong relationships between modular programs as well as between traditional programs. We show how the notion of a conservative extension can be used to justify the common projection rewriting.

scholarly journals Composing programs in a rewriting logic for declarative programming

2003 ◽  
Vol 3 (2) ◽  
pp. 189-221 ◽  
Author(s):  
J. M. MOLINA-BRAVO ◽  
E. PIMENTEL
Keyword(s):  
Logic Programming ◽  
Declarative Programming ◽  
Rewriting Logic ◽  
Logic Programs ◽  
Alternative Semantics ◽  
Program Module ◽  
First Order ◽  
Natural Notion ◽  
Functional Logic ◽  
Simple Notion

Constructor-Based Conditional Rewriting Logic is a general framework for integrating first-order functional and logic programming which gives an algebraic semantics for nondeterministic functional-logic programs. In the context of this formalism, we introduce a simple notion of program module as an open program which can be extended together with several mechanisms to combine them. These mechanisms are based on a reduced set of operations. However, the high expressiveness of these operations enable us to model typical constructs for program modularization like hiding, export/import, genericity/instantiation, and inheritance in a simple way. We also deal with the semantic aspects of the proposal by introducing an immediate consequence operator, and studying several alternative semantics for a program module, based on this operator, in the line of logic programming: the operator itself, its least fixpoint (the least model of the module), the set of its pre-fixpoints (term models of the module), and some other variations in order to find a compositional and fully abstract semantics w.r.t. the set of operations and a natural notion of observability.

scholarly journals Representing first-order causal theories by logic programs

2011 ◽  
Vol 12 (3) ◽  
pp. 383-412 ◽  
Author(s):  
PAOLO FERRARIS ◽  
JOOHYUNG LEE ◽  
YULIYA LIERLER ◽  
VLADIMIR LIFSCHITZ ◽  
FANGKAI YANG
Keyword(s):  
Artificial Intelligence ◽  
Logic Programming ◽  
Logic Programs ◽  
Action Languages ◽  
First Order ◽  
National Conference ◽  
Theories Of Action ◽  
Causal Theories ◽  
Causal Logic ◽  
The Way

AbstractNonmonotonic causal logic, introduced by McCain and Turner (McCain, N. and Turner, H. 1997. Causal theories of action and change. In Proceedings of National Conference on Artificial Intelligence (AAAI), Stanford, CA, 460–465) became the basis for the semantics of several expressive action languages. McCain's embedding of definite propositional causal theories into logic programming paved the way to the use of answer set solvers for answering queries about actions described in such languages. In this paper we extend this embedding to nondefinite theories and to the first-order causal logic.

Topological Model Set Deformations in Logic Programming

1989 ◽  
Vol 12 (3) ◽  
pp. 357-399
Author(s):  
Aida Batarekh ◽  
V.S. Subrahmanian
Keyword(s):  
Logic Programming ◽  
Sufficient Conditions ◽  
Topological Spaces ◽  
Logic Programs ◽  
First Order ◽  
Order Language ◽  
Language L ◽  
General Logic ◽  
Model Set ◽  
Necessary And Sufficient

Given a first order language L, and a notion of a logic L w.r.t. L, we investigate the topological properties of the space of L-structures for L. We show that under a topology called the query topology which arises naturally in logic programming, the space of L-models (where L is a decent logic) of any sentence (set of clauses) in L may be regarded as a (closed, compact) T4-space. We then investigate the properties of maps from structures to structures. Our results allow us to apply various well-known results on the fixed-points of operators on topological spaces to the semantics of logic programming – in particular, we are able to derive necessary and sufficient topological conditions for the completion of covered general logic programs to be consistent. Moreover, we derive sufficient conditions guaranteeing the consistency of program completions, and for logic programs to be determinate. We also apply our results to characterize consistency of the unions of program completions.

scholarly journals In Praise of Impredicativity: A Contribution to the Formalization of Meta-Programming

2019 ◽  
Vol 20 (1) ◽  
pp. 99-146 ◽  
Author(s):  
FRANÇOIS BRY
Keyword(s):  
Logic Programming ◽  
Functional Programming ◽  
Predicate Logic ◽  
Order Logic ◽  
Declarative Programming ◽  
Conservative Extension ◽  
First Order ◽  
Meta Programming ◽  
Programming Techniques ◽  
Higher Order Functions

AbstractProcessing programs as data is one of the successes of functional and logic programming. Higher-order functions, as program-processing programs are called in functional programming, and meta-programs, as they are called in logic programming, are widespread declarative programming techniques. In logic programming, there is a gap between the meta-programming practice and its theory: The formalizations of meta-programming do not explicitly address its impredicativity and are not fully adequate. This article aims at overcoming this unsatisfactory situation by discussing the relevance of impredicativity to meta-programming, by revisiting former formalizations of meta-programming, and by defining Reflective Predicate Logic, a conservative extension of first-order logic, which provides a simple formalization of meta-programming.

scholarly journals Decidability of the Clark's completion semantics for monadic programs and queries

2014 ◽  
Vol 15 (3) ◽  
pp. 402-412
Author(s):  
LEVON HAYKAZYAN
Keyword(s):  
Logic Programming ◽  
Logic Programs ◽  
First Order ◽  
Order Language ◽  
General Logic ◽  
Turing Complete

AbstractThere are many different semantics for general logic programs (i.e. programs that use negation in the bodies of clauses). Most of these semantics are Turing complete (in a sense that can be made precise), implying that they are undecidable. To obtain decidability one needs to put additional restrictions on programs and queries. In logic programming it is natural to put restrictions on the underlying first-order language. In this note, we show the decidability of the Clark's completion semantics for monadic general programs and queries.

Relativized realizability in intuitionistic arithmetic of all finite types

1978 ◽  
Vol 43 (1) ◽  
pp. 23-44 ◽  
Author(s):  
Nicolas D. Goodman
Keyword(s):  
Extension Theorem ◽  
General Notion ◽  
Conservative Extension ◽  
First Order ◽  
New Information ◽  
Reflection Theorem ◽  
Order Arithmetic ◽  
Special Case ◽  
Dependent Choice ◽  
Intuitionistic Arithmetic

In this paper we introduce a new notion of realizability for intuitionistic arithmetic in all finite types. The notion seems to us to capture some of the intuition underlying both the recursive realizability of Kjeene [5] and the semantics of Kripke [7]. After some preliminaries of a syntactic and recursion-theoretic character in §1, we motivate and define our notion of realizability in §2. In §3 we prove a soundness theorem, and in §4 we apply that theorem to obtain new information about provability in some extensions of intuitionistic arithmetic in all finite types. In §5 we consider a special case of our general notion and prove a kind of reflection theorem for it. Finally, in §6, we consider a formalized version of our realizability notion and use it to give a new proof of the conservative extension theorem discussed in Goodman and Myhill [4] and proved in our [3]. (Apparently, a form of this result is also proved in Mine [13]. We have not seen this paper, but are relying on [12].) As a corollary, we obtain the following somewhat strengthened result: Let Σ be any extension of first-order intuitionistic arithmetic (HA) formalized in the language of HA. Let Σω be the theory obtained from Σ by adding functionals of finite type with intuitionistic logic, intensional identity, and axioms of choice and dependent choice at all types. Then Σω is a conservative extension of Σ. An interesting example of this theorem is obtained by taking Σ to be classical first-order arithmetic.

Underlying Common Factors of Adolescent Problem Behaviors

2002 ◽  
Vol 29 (2) ◽  
pp. 161-182 ◽  
Author(s):  
Lening Zhang ◽  
John W. Welte ◽  
William F. Wieczorek
Keyword(s):  
Problem Behaviors ◽  
Latent Variable ◽  
Factor Model ◽  
Common Factor ◽  
Measurement Model ◽  
First Order ◽  
Adolescent Problem Behaviors ◽  
The Common ◽  
Order Factor ◽  
Second Order Factor Analysis

The Buffalo Longitudinal Study of Young Men was used to address the possibility of a common factor underlying adolescent problem behaviors. First, a measurement model with a single first-order factor was compared to a model with three separate correlated first-order factors. The three-factor model was better supported, making it logical to conduct a second-order factor analysis, which confirmed the logic. Second, a substantive model was estimated in each of two waves with psychopathic state as the common factor predicting drinking, drug use, and delinquency. Psychopathic state was stable across waves. The theory that a single latent variable accounts for large covariance among adolescent problem behaviors was supported.

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