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Logic Programming and Knowledge Representation
 Journal of Logic Programming
, 1994
"... In this paper, we review recent work aimed at the application of declarative logic programming to knowledge representation in artificial intelligence. We consider exten sions of the language of definite logic programs by classical (strong) negation, disjunc tion, and some modal operators and sh ..."
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Cited by 224 (21 self)
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In this paper, we review recent work aimed at the application of declarative logic programming to knowledge representation in artificial intelligence. We consider exten sions of the language of definite logic programs by classical (strong) negation, disjunc tion, and some modal operators and show how each of the added features extends the representational power of the language.
Linear Objects: logical processes with builtin inheritance
, 1990
"... We present a new framework for amalgamating two successful programming paradigms: logic programming and objectoriented programming. From the former, we keep the declarative reading of programs. From the latter, we select two crucial notions: (i) the ability for objects to dynamically change their ..."
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Cited by 205 (6 self)
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We present a new framework for amalgamating two successful programming paradigms: logic programming and objectoriented programming. From the former, we keep the declarative reading of programs. From the latter, we select two crucial notions: (i) the ability for objects to dynamically change their internal state during the computation; (ii) the structured representation of knowledge, generally obtained via inheritance graphs among classes of objects. We start with the approach, introduced in concurrent logic programming languages, which identifies objects with proof processes and object states with arguments occurring in the goals of a given process. This provides a clean, sideeffect free account of the dynamic behavior of objects in terms of the search tree  the only dynamic entity in logic programming languages. We integrate this view of objects with an extension of logic programming, which we call Linear Objects, based on the possibility of having multiple literals in the head of a program clause. This contains within itself the basis for a flexible form of inheritance, and maintains the constructive property of Prolog of returning definite answer substitutions as output of the proof of nonground goals. The theoretical background for Linear Objects is Linear Logic, a logic recently introduced to provide a theoretical basis for the study of concurrency. We also show that Linear Objects can be considered a constructive restriction of full Classical Logic. We illustrate the expressive power of Linear Objects compared to Prolog by several examples from the objectoriented domain, but we also show that it can be used to provide elegant solutions for problems arising in the standard style of logic programming.
Logic and Databases: a 20 Year Retrospective
, 1996
"... . At a workshop held in Toulouse, France in 1977, Gallaire, Minker and Nicolas stated that logic and databases was a field in its own right (see [131]). This was the first time that this designation was made. The impetus for this started approximately twenty years ago in 1976 when I visited Gallaire ..."
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Cited by 55 (1 self)
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. At a workshop held in Toulouse, France in 1977, Gallaire, Minker and Nicolas stated that logic and databases was a field in its own right (see [131]). This was the first time that this designation was made. The impetus for this started approximately twenty years ago in 1976 when I visited Gallaire and Nicolas in Toulouse, France, which culminated in a workshop held in Toulouse, France in 1977. It is appropriate, then to provide an assessment as to what has been achieved in the twenty years since the field started as a distinct discipline. In this retrospective I shall review developments that have taken place in the field, assess the contributions that have been made, consider the status of implementations of deductive databases and discuss the future of work in this area. 1 Introduction As described in [234], the use of logic and deduction in databases started in the late 1960s. Prominent among the developments was the work by Levien and Maron [202, 203, 199, 200, 201] and Kuhns [1...
PROTEIN: A PROver with a Theory Extension Interface
 AUTOMATED DEDUCTION  CADE12, VOLUME 814 OF LNAI
, 1994
"... PROTEIN (PROver with a Theory Extension INterface) is a PTTPbased first order theorem prover over builtin theories. Besides various standardrefinements known for model elimination, PROTEIN also offers a variant of model elimination for casebased reasoning and which does not need contrapositives. ..."
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Cited by 41 (10 self)
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PROTEIN (PROver with a Theory Extension INterface) is a PTTPbased first order theorem prover over builtin theories. Besides various standardrefinements known for model elimination, PROTEIN also offers a variant of model elimination for casebased reasoning and which does not need contrapositives.
Uniform Proofs and Disjunctive Logic Programming (Extended Abstract)
, 1995
"... ) y Gopalan Nadathur z Donald W. Loveland Department of Computer Science Department of Computer Science University of Chicago Duke University 1100 E 58th Street, Chicago, IL 60637 Box 90129, Durham, NC 277080129 gopalan@cs.uchicago.edu dwl@cs.duke.edu Abstract One formulation of the concept of ..."
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Cited by 10 (3 self)
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) y Gopalan Nadathur z Donald W. Loveland Department of Computer Science Department of Computer Science University of Chicago Duke University 1100 E 58th Street, Chicago, IL 60637 Box 90129, Durham, NC 277080129 gopalan@cs.uchicago.edu dwl@cs.duke.edu Abstract One formulation of the concept of logic programming is the notion of Abstract Logic Programming Language, introduced in [8]. Central to that definition is uniform proof, which enforces the requirements of inference direction, including goaldirectedness, and the duality of readings, declarative and procedural. We use this technology to investigate Disjunctive Logic Programming (DLP), an extension of traditional logic programming that permits disjunctive program clauses. This extension has been considered by some to be inappropriately identified with logic programming because the indefinite reasoning introduced by disjunction violates the goaloriented search directionality central to logic programming. We overcome this crit...
Computing Answers with Model Elimination
, 1997
"... We demonstrate that theorem provers using model elimination (ME) can be used as answercomplete interpreters for disjunctive logic programming. More specifically, we introduce a mechanism for computing answers into the restart variant of ME. Building on this we develop a new calculus called ancestry ..."
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Cited by 9 (2 self)
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We demonstrate that theorem provers using model elimination (ME) can be used as answercomplete interpreters for disjunctive logic programming. More specifically, we introduce a mechanism for computing answers into the restart variant of ME. Building on this we develop a new calculus called ancestry restart ME. This variant admits a more restrictive regularity restriction than restart ME, and, as a side effect, it is in particular attractive for computing definite answers. The presented calculi can also be used successfully in the context of automated theorem proving. We demonstrate experimentally that it is more difficult to compute (nontrivial) answers to goals, instead of only proving the existence of answers. Keywords. Automated reasoning; theorem proving; model elimination; logic programming; computing answers. In first order automatic theorem proving one is interested in the question whether a given formula follows logically from a set of axioms. This is a rather artificial t...
Refinements of Theory Model Elimination and a Variant without Contrapositives
 University of Koblenz, Institute for Computer Science
, 1994
"... Theory Reasoning means to buildin certain knowledge about a problem domain into a deduction system or calculus, which is in our case model elimination. Several versions of theory model elimination (TME) calculi are presented and proven complete: on the one hand we have highly restricted versions of ..."
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Cited by 8 (6 self)
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Theory Reasoning means to buildin certain knowledge about a problem domain into a deduction system or calculus, which is in our case model elimination. Several versions of theory model elimination (TME) calculi are presented and proven complete: on the one hand we have highly restricted versions of total and partial TME. These restrictions allow (1) to keep fewer path literals in extension steps than in related calculi, and (2) discard proof attempts with multiple occurrences of literals along a path (i.e. regularity holds). On the other hand, we obtain by small modifications to TME versions which do not need contrapositives (a la NearHorn Prolog). We show that regularity can be adapted for these versions. The independence of the goal computation rule holds for all variants. Comparative runtime results for our PTTPimplementations are supplied. 1 Introduction The model elimination calculus (ME calculus) has been developed already in the early days of automated theorem proving [Lovel...
An Alternative Characterization of Disjunctive Logic Programs
 LOGIC PROGRAMMING: PROC. OF THE 1991 INT'L SYMP
, 1991
"... We present an alternative characterization of disjunctive logic programs. We first review Inheritance nearHorn Prolog (InHProlog), an intuitive and computationally effective procedure that extends Prolog using caseanalysis. We then describe a fixpoint characterization of disjunctive logic program ..."
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Cited by 8 (1 self)
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We present an alternative characterization of disjunctive logic programs. We first review Inheritance nearHorn Prolog (InHProlog), an intuitive and computationally effective procedure that extends Prolog using caseanalysis. We then describe a fixpoint characterization of disjunctive logic programs that is similarly based on caseanalysis. This fixpoint characterization closely corresponds to the InHProlog procedure, and so gives needed insight into the difficult problem of recognizing the minimal disjunctive answers obtainable from the procedure. Due to its caseanalysis nature, this characterization maintains a natural and close relationship to the standard characterization of Horn programs. It also gives added insight into the role of definite answers for disjunctive programs and enables one to neatly focus attention on the interesting class of definite (single atom) consequences.
The Complexity Of Querying Indefinite Information: Defined Relations, Recursion And Linear Order
, 1992
"... OF THE DISSERTATION The Complexity of Querying Indefinite Information: Defined Relations, Recursion and Linear Order by Ronald van der Meyden, Ph.D. Dissertation Director: L.T. McCarty This dissertation studies the computational complexity of answering queries in logical databases containing indefin ..."
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Cited by 7 (0 self)
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OF THE DISSERTATION The Complexity of Querying Indefinite Information: Defined Relations, Recursion and Linear Order by Ronald van der Meyden, Ph.D. Dissertation Director: L.T. McCarty This dissertation studies the computational complexity of answering queries in logical databases containing indefinite information arising from two sources: facts stated in terms of defined relations, and incomplete information about linearly ordered domains. First, we consider databases consisting of (1) a DATALOG program and (2) a description of the world in terms of the predicates defined by the program as well as the basic predicates. The query processing problem in such databases is related to issues in database theory, including view updates and DATALOG optimization, and also to the Artificial Intelligence problems of reasoning in circumscribed theories and sceptical abductive reasoning. If the program is nonrecursive, the meaning of the database can be represented by Clark's Predicate Completion,...
Uniform Provability in Classical Logic
 Journal of Logic and Computation
, 1996
"... Uniform proofs are sequent calculus proofs with the following characteristic: the last step in the derivation of a complex formula at any stage in the proof is always the introduction of the toplevel logical symbol of that formula. We investigate the relevance of this uniform proof notion to struct ..."
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Cited by 7 (1 self)
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Uniform proofs are sequent calculus proofs with the following characteristic: the last step in the derivation of a complex formula at any stage in the proof is always the introduction of the toplevel logical symbol of that formula. We investigate the relevance of this uniform proof notion to structuring proof search in classical logic. A logical language in whose context provability is equivalent to uniform provability admits of a goaldirected proof procedure that interprets logical symbols as search directives whose meanings are given by the corresponding inference rules. While this uniform provability property does not hold directly of classical logic, we show that it holds of a fragment of it that only excludes essentially positive occurrences of universal quantifiers under a modest, sound, modification to the set of assumptions: the addition to them of the negation of the formula being proved. We further note that all uses of the added formula can be factored into certain derived...