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Model counting is the problem of computing the number of models that satisfy a given propositional theory. It has recently been applied to solving inference tasks in probabilistic logic programming, where the goal is to compute the probability of given queries being true provided a set of mutually independent random variables, a model (a logic program) and some evidence. The core of solving this inference task involves translating the logic program to a propositional theory and using a model counter. In this paper, we show that for some problems that involve inductive definitions like reachability in a graph, the translation of logic programs to SAT can be expensive for the purpose of solving inference tasks. For such problems, direct implementation of stable model semantics allows for more efficient solving. We present two implementation techniques, based on unfounded set detection, that extend a propositional model counter to a stable model counter. Our experiments show that for particular problems, our approach can outperform a state-of-the-art probabilistic logic programming solver by several orders of magnitude in terms of running time and space requirements, and can solve instances of significantly larger sizes on which the current solver runs out of time or memory.

The Journal of Logic and Algebraic Programming 1999: Volume 38 , Issue CONTENTS. Digitized from IA1652909-05 . Previous issue: sim_journal-of-logic-and-algebraic-programming_1999_38_index . Next issue: sim_journal-of-logic-and-algebraic-programming_1999-01_38_1 . Note: This issue has no cover

The Journal of Logic and Algebraic Programming 1999: Volume 38 , Issue CONTENTS. Digitized from IA1652909-05 . Previous issue: sim_journal-of-logic-and-algebraic-programming_1999_38_index . Next issue: sim_journal-of-logic-and-algebraic-programming_1999-01_38_1 . Note: This issue has no cover

The Journal of Logic and Algebraic Programming 1999: Volume 41 , Issue Index. Digitized from IA1652909-05 . Previous issue: sim_journal-of-logic-and-algebraic-programming_august-september-1999_40_2-3 . Next issue: sim_journal-of-logic-and-algebraic-programming_1999_41_contents . Note: This issue has no cover

The Journal of Logic and Algebraic Programming 1999: Volume 41 , Issue Index. Digitized from IA1652909-05 . Previous issue: sim_journal-of-logic-and-algebraic-programming_august-september-1999_40_2-3 . Next issue: sim_journal-of-logic-and-algebraic-programming_1999_41_contents . Note: This issue has no cover

In designing the interface between a database and a logic system with inference such as Prolog, efficiency is the major issue. Presented here are three of the methods that are considered most promising and in which much research is focused. The first method explores extending an inference machine to include a database manager, the second couples the inference mechanism with a database management system; and the third extends a database management mechanism to include inference. Acknowledging up front that no method can be claimed best, the major emphasis of this study will be to determine the strengths and limitations of all three methods and thereby help to clarify many uncertain and sometimes conflicting issues caused by the parallel lines of development from the database and artificial intelligence communities.

In designing the interface between a database and a logic system with inference such as Prolog, efficiency is the major issue. Presented here are three of the methods that are considered most promising and in which much research is focused. The first method explores extending an inference machine to include a database manager, the second couples the inference mechanism with a database management system; and the third extends a database management mechanism to include inference. Acknowledging up front that no method can be claimed best, the major emphasis of this study will be to determine the strengths and limitations of all three methods and thereby help to clarify many uncertain and sometimes conflicting issues caused by the parallel lines of development from the database and artificial intelligence communities.

The Journal of Logic and Algebraic Programming 1996: Volume 27 , Issue CONTENTS. Digitized from IA1652909-05 . Previous issue: sim_journal-of-logic-and-algebraic-programming_1996_27_index . Next issue: sim_journal-of-logic-and-algebraic-programming_1996-04_27_1 . Note: This issue has no cover

The Journal of Logic and Algebraic Programming 1996: Volume 27 , Issue CONTENTS. Digitized from IA1652909-05 . Previous issue: sim_journal-of-logic-and-algebraic-programming_1996_27_index . Next issue: sim_journal-of-logic-and-algebraic-programming_1996-04_27_1 . Note: This issue has no cover

The Journal of Logic and Algebraic Programming 1997: Volume 30 , Issue Index. Digitized from IA1652909-05 . Previous issue: sim_journal-of-logic-and-algebraic-programming_october-december-1996_29_1-3 . Next issue: sim_journal-of-logic-and-algebraic-programming_1997_30_contents . Note: This issue has no cover

This volume contains the papers presented at Arg-LPNMR 2016: First International Workshop on Argumentation in Logic Programming and Nonmonotonic Reasoning held on July 8-10, 2016 in New York City, NY.

The Journal of Logic and Algebraic Programming 1996: Volume 29 , Issue CONTENTS. Digitized from IA1652909-05 . Previous issue: sim_journal-of-logic-and-algebraic-programming_1996_29_index . Next issue: sim_journal-of-logic-and-algebraic-programming_october-december-1996_29_1-3 .

The Journal of Logic and Algebraic Programming 1997: Volume 31 , Issue Index. Digitized from IA1652909-05 . Previous issue: sim_journal-of-logic-and-algebraic-programming_1997-03_30_3 . Next issue: sim_journal-of-logic-and-algebraic-programming_1997_31_contents . Note: This issue has no cover

The Journal of Logic and Algebraic Programming 1998: Volume 34 , Issue Index. Digitized from IA1652909-05 . Previous issue: sim_journal-of-logic-and-algebraic-programming_1997-12_33_3 . Next issue: sim_journal-of-logic-and-algebraic-programming_1998_34_contents . Note: This issue has no cover

The Journal of Logic and Algebraic Programming 1998: Volume 34 , Issue Index. Digitized from IA1652909-05 . Previous issue: sim_journal-of-logic-and-algebraic-programming_1997-12_33_3 . Next issue: sim_journal-of-logic-and-algebraic-programming_1998_34_contents . Note: This issue has no cover

The Journal of Logic and Algebraic Programming 1998: Volume 34 , Issue Index. Digitized from IA1652909-05 . Previous issue: sim_journal-of-logic-and-algebraic-programming_1997-12_33_3 . Next issue: sim_journal-of-logic-and-algebraic-programming_1998_34_contents . Note: This issue has no cover

The Journal of Logic and Algebraic Programming 1998: Volume 34 , Issue Index. Digitized from IA1652909-05 . Previous issue: sim_journal-of-logic-and-algebraic-programming_1997-12_33_3 . Next issue: sim_journal-of-logic-and-algebraic-programming_1998_34_contents . Note: This issue has no cover

The Journal of Logic and Algebraic Programming 1998: Volume 34 , Issue Index. Digitized from IA1652909-05 . Previous issue: sim_journal-of-logic-and-algebraic-programming_1997-12_33_3 . Next issue: sim_journal-of-logic-and-algebraic-programming_1998_34_contents . Note: This issue has no cover

The Journal of Logic and Algebraic Programming 1998: Volume 34 , Issue Index. Digitized from IA1652909-05 . Previous issue: sim_journal-of-logic-and-algebraic-programming_1997-12_33_3 . Next issue: sim_journal-of-logic-and-algebraic-programming_1998_34_contents . Note: This issue has no cover

The Journal of Logic and Algebraic Programming 1998: Volume 34 , Issue Index. Digitized from IA1652909-05 . Previous issue: sim_journal-of-logic-and-algebraic-programming_1997-12_33_3 . Next issue: sim_journal-of-logic-and-algebraic-programming_1998_34_contents . Note: This issue has no cover

The Journal of Logic and Algebraic Programming 1998: Volume 34 , Issue Index. Digitized from IA1652909-05 . Previous issue: sim_journal-of-logic-and-algebraic-programming_1997-12_33_3 . Next issue: sim_journal-of-logic-and-algebraic-programming_1998_34_contents . Note: This issue has no cover

FASILL (acronym of "Fuzzy Aggregators and Similarity Into a Logic Language") is a fuzzy logic programming language with implicit/explicit truth degree annotations, a great variety of connectives and unification by similarity. FASILL integrates and extends features coming from MALP (Multi-Adjoint Logic Programming, a fuzzy logic language with explicitly annotated rules) and Bousi~Prolog (which uses a weak unification algorithm and is well suited for flexible query answering). Hence, it properly manages similarity and truth degrees in a single framework combining the expressive benefits of both languages. This paper presents the main features and implementations details of FASILL. Along the paper we describe its syntax and operational semantics and we give clues of the implementation of the lattice module and the similarity module, two of the main building blocks of the new programming environment which enriches the FLOPER system developed in our research group.

The Journal of Logic and Algebraic Programming 1998: Volume 35 , Issue Index. Digitized from IA1652909-05 . Previous issue: sim_journal-of-logic-and-algebraic-programming_1998-03_34_3 . Next issue: sim_journal-of-logic-and-algebraic-programming_1998_35_contents . Note: This issue has no cover

With sound unification, Definite Clause Grammars and compact expression of combinatorial generation algorithms, logic programming is shown to conveniently host a declarative playground where interesting properties and behaviors emerge from the interaction of heterogenous but deeply connected computational objects. Compact combinatorial generation algorithms are given for several families of lambda terms, including open, closed, simply typed and linear terms as well as type inference and normal order reduction algorithms. We describe a Prolog-based combined lambda term generator and type-inferrer for closed well-typed terms of a given size, in de Bruijn notation. We introduce a compressed de Bruijn representation of lambda terms and define its bijections to standard representations. Our compressed terms facilitate derivation of size-proportionate ranking and unranking algorithms of lambda terms and their inferred simple types. The S and K combinator expressions form a well-known Turing-complete subset of the lambda calculus. We specify evaluation, type inference and combinatorial generation algorithms for SK-combinator trees. In the process, we unravel properties shedding new light on interesting aspects of their structure and distribution. A uniform representation, as binary trees with empty leaves, is given to expressions built with Rosser's X-combinator, natural numbers, lambda terms and simple types. Using this shared representation, ranking/unranking algorithm of lambda terms to tree-based natural numbers are described. Our algorithms, expressed as an incrementally developed literate Prolog program, implement a declarative playground for exploration of representations, encodings and computations with uniformly represented lambda terms, types, combinators and tree-based arithmetic.

With sound unification, Definite Clause Grammars and compact expression of combinatorial generation algorithms, logic programming is shown to conveniently host a declarative playground where interesting properties and behaviors emerge from the interaction of heterogenous but deeply connected computational objects. Compact combinatorial generation algorithms are given for several families of lambda terms, including open, closed, simply typed and linear terms as well as type inference and normal order reduction algorithms. We describe a Prolog-based combined lambda term generator and type-inferrer for closed well-typed terms of a given size, in de Bruijn notation. We introduce a compressed de Bruijn representation of lambda terms and define its bijections to standard representations. Our compressed terms facilitate derivation of size-proportionate ranking and unranking algorithms of lambda terms and their inferred simple types. The S and K combinator expressions form a well-known Turing-complete subset of the lambda calculus. We specify evaluation, type inference and combinatorial generation algorithms for SK-combinator trees. In the process, we unravel properties shedding new light on interesting aspects of their structure and distribution. A uniform representation, as binary trees with empty leaves, is given to expressions built with Rosser's X-combinator, natural numbers, lambda terms and simple types. Using this shared representation, ranking/unranking algorithm of lambda terms to tree-based natural numbers are described. Our algorithms, expressed as an incrementally developed literate Prolog program, implement a declarative playground for exploration of representations, encodings and computations with uniformly represented lambda terms, types, combinators and tree-based arithmetic.

In this thesis, we present two approaches to a rigorous mathematical and algorithmic foundation of quantitative and statistical inference in constraint-based natural language processing. The first approach, called quantitative constraint logic programming, is conceptualized in a clear logical framework, and presents a sound and complete system of quantitative inference for definite clauses annotated with subjective weights. This approach combines a rigorous formal semantics for quantitative inference based on subjective weights with efficient weight-based pruning for constraint-based systems. The second approach, called probabilistic constraint logic programming, introduces a log-linear probability distribution on the proof trees of a constraint logic program and an algorithm for statistical inference of the parameters and properties of such probability models from incomplete, i.e., unparsed data. The possibility of defining arbitrary properties of proof trees as properties of the log-linear probability model and efficiently estimating appropriate parameter values for them permits the probabilistic modeling of arbitrary context-dependencies in constraint logic programs. The usefulness of these ideas is evaluated empirically in a small-scale experiment on finding the correct parses of a constraint-based grammar. In addition, we address the problem of computational intractability of the calculation of expectations in the inference task and present various techniques to approximately solve this task. Moreover, we present an approximate heuristic technique for searching for the most probable analysis in probabilistic constraint logic programs.

In this thesis, we present two approaches to a rigorous mathematical and algorithmic foundation of quantitative and statistical inference in constraint-based natural language processing. The first approach, called quantitative constraint logic programming, is conceptualized in a clear logical framework, and presents a sound and complete system of quantitative inference for definite clauses annotated with subjective weights. This approach combines a rigorous formal semantics for quantitative inference based on subjective weights with efficient weight-based pruning for constraint-based systems. The second approach, called probabilistic constraint logic programming, introduces a log-linear probability distribution on the proof trees of a constraint logic program and an algorithm for statistical inference of the parameters and properties of such probability models from incomplete, i.e., unparsed data. The possibility of defining arbitrary properties of proof trees as properties of the log-linear probability model and efficiently estimating appropriate parameter values for them permits the probabilistic modeling of arbitrary context-dependencies in constraint logic programs. The usefulness of these ideas is evaluated empirically in a small-scale experiment on finding the correct parses of a constraint-based grammar. In addition, we address the problem of computational intractability of the calculation of expectations in the inference task and present various techniques to approximately solve this task. Moreover, we present an approximate heuristic technique for searching for the most probable analysis in probabilistic constraint logic programs.

In this thesis, we present two approaches to a rigorous mathematical and algorithmic foundation of quantitative and statistical inference in constraint-based natural language processing. The first approach, called quantitative constraint logic programming, is conceptualized in a clear logical framework, and presents a sound and complete system of quantitative inference for definite clauses annotated with subjective weights. This approach combines a rigorous formal semantics for quantitative inference based on subjective weights with efficient weight-based pruning for constraint-based systems. The second approach, called probabilistic constraint logic programming, introduces a log-linear probability distribution on the proof trees of a constraint logic program and an algorithm for statistical inference of the parameters and properties of such probability models from incomplete, i.e., unparsed data. The possibility of defining arbitrary properties of proof trees as properties of the log-linear probability model and efficiently estimating appropriate parameter values for them permits the probabilistic modeling of arbitrary context-dependencies in constraint logic programs. The usefulness of these ideas is evaluated empirically in a small-scale experiment on finding the correct parses of a constraint-based grammar. In addition, we address the problem of computational intractability of the calculation of expectations in the inference task and present various techniques to approximately solve this task. Moreover, we present an approximate heuristic technique for searching for the most probable analysis in probabilistic constraint logic programs.

In recent work, semantic games of independence-friendly logic were studied in strategic form in terms of (mixed strategy) Nash equilibria. The class of strategic games of independence-friendly logic is contained in the class of win-loss, zero-sum two-player games. In this note we draw on the theory of linear programming to develop tools to analyze the value of such games. We give two applications of these tools to independence-friendly logic under the so-called equilibrium semantics.

In recent work, semantic games of independence-friendly logic were studied in strategic form in terms of (mixed strategy) Nash equilibria. The class of strategic games of independence-friendly logic is contained in the class of win-loss, zero-sum two-player games. In this note we draw on the theory of linear programming to develop tools to analyze the value of such games. We give two applications of these tools to independence-friendly logic under the so-called equilibrium semantics.

In recent work, semantic games of independence-friendly logic were studied in strategic form in terms of (mixed strategy) Nash equilibria. The class of strategic games of independence-friendly logic is contained in the class of win-loss, zero-sum two-player games. In this note we draw on the theory of linear programming to develop tools to analyze the value of such games. We give two applications of these tools to independence-friendly logic under the so-called equilibrium semantics.

The Journal of Logic and Algebraic Programming 1998: Volume 36 , Issue Index. Digitized from IA1652909-05 . Previous issue: sim_journal-of-logic-and-algebraic-programming_1998-06_35_3 . Next issue: sim_journal-of-logic-and-algebraic-programming_1998_36_contents . Note: This issue has no cover

The Journal of Logic and Algebraic Programming 1998: Volume 36 , Issue Index. Digitized from IA1652909-05 . Previous issue: sim_journal-of-logic-and-algebraic-programming_1998-06_35_3 . Next issue: sim_journal-of-logic-and-algebraic-programming_1998_36_contents . Note: This issue has no cover

The Journal of Logic and Algebraic Programming 1998: Volume 36 , Issue Index. Digitized from IA1652909-05 . Previous issue: sim_journal-of-logic-and-algebraic-programming_1998-06_35_3 . Next issue: sim_journal-of-logic-and-algebraic-programming_1998_36_contents . Note: This issue has no cover

The Journal of Logic and Algebraic Programming 1998: Volume 36 , Issue Index. Digitized from IA1652909-05 . Previous issue: sim_journal-of-logic-and-algebraic-programming_1998-06_35_3 . Next issue: sim_journal-of-logic-and-algebraic-programming_1998_36_contents . Note: This issue has no cover

The Journal of Logic and Algebraic Programming 1998: Volume 36 , Issue Index. Digitized from IA1652909-05 . Previous issue: sim_journal-of-logic-and-algebraic-programming_1998-06_35_3 . Next issue: sim_journal-of-logic-and-algebraic-programming_1998_36_contents . Note: This issue has no cover

The Journal of Logic and Algebraic Programming 1998: Volume 36 , Issue Index. Digitized from IA1652909-05 . Previous issue: sim_journal-of-logic-and-algebraic-programming_1998-06_35_3 . Next issue: sim_journal-of-logic-and-algebraic-programming_1998_36_contents . Note: This issue has no cover

1 v. (various pagings) 28 cm

1 v. (various pagings) 28 cm

This papers develops a logical language for representing probabilistic causal laws. Our interest in such a language is twofold. First, it can be motivated as a fundamental study of the representation of causal knowledge. Causality has an inherent dynamic aspect, which has been studied at the semantical level by Shafer in his framework of probability trees. In such a dynamic context, where the evolution of a domain over time is considered, the idea of a causal law as something which guides this evolution is quite natural. In our formalization, a set of probabilistic causal laws can be used to represent a class of probability trees in a concise, flexible and modular way. In this way, our work extends Shafer's by offering a convenient logical representation for his semantical objects. Second, this language also has relevance for the area of probabilistic logic programming. In particular, we prove that the formal semantics of a theory in our language can be equivalently defined as a probability distribution over the well-founded models of certain logic programs, rendering it formally quite similar to existing languages such as ICL or PRISM. Because we can motivate and explain our language in a completely self-contained way as a representation of probabilistic causal laws, this provides a new way of explaining the intuitions behind such probabilistic logic programs: we can say precisely which knowledge such a program expresses, in terms that are equally understandable by a non-logician. Moreover, we also obtain an additional piece of knowledge representation methodology for probabilistic logic programs, by showing how they can express probabilistic causal laws.

This papers develops a logical language for representing probabilistic causal laws. Our interest in such a language is twofold. First, it can be motivated as a fundamental study of the representation of causal knowledge. Causality has an inherent dynamic aspect, which has been studied at the semantical level by Shafer in his framework of probability trees. In such a dynamic context, where the evolution of a domain over time is considered, the idea of a causal law as something which guides this evolution is quite natural. In our formalization, a set of probabilistic causal laws can be used to represent a class of probability trees in a concise, flexible and modular way. In this way, our work extends Shafer's by offering a convenient logical representation for his semantical objects. Second, this language also has relevance for the area of probabilistic logic programming. In particular, we prove that the formal semantics of a theory in our language can be equivalently defined as a probability distribution over the well-founded models of certain logic programs, rendering it formally quite similar to existing languages such as ICL or PRISM. Because we can motivate and explain our language in a completely self-contained way as a representation of probabilistic causal laws, this provides a new way of explaining the intuitions behind such probabilistic logic programs: we can say precisely which knowledge such a program expresses, in terms that are equally understandable by a non-logician. Moreover, we also obtain an additional piece of knowledge representation methodology for probabilistic logic programs, by showing how they can express probabilistic causal laws.

The field of Artificial Intelligence strives to produce computer programs that exhibit intelligent behavior. One of the areas of interest is the processing of natural language. This report will discuss the role of the computer language PROLOG in Natural Language Processing (NLP) both from theoretic and pragmatic viewpoints. The reasons for using PROLOG for NLP are numerous. First, linguists can write natural language grammars almost directly as PROLOG programs; this allows 'fast-prototyping' of NLP systems and facilitates analysis of NLP theories. Second, semantic representations of natural language texts that use logic formalisms are readily produced in PROLOG because of PROLOG's logical foundations. Third, PROLOG's built-in inferencing mechanisms are often sufficient for inferences on the logical forms produced by NLPs. Fourth, the logical, declarative nature of PROLOG may make it the language of choice for parallel computing systems. Finally, the fact that PROLOG has a de facto standard (Edinburgh) makes the porting of code from one computer system to another virtually trouble free. Perhaps the strongest tie one could make between NLP and PROLOG was stated by John Stuart Mill in his inaugural Address at St. Andrews: The structure of every sentence is a lesson in logic.

Approved F.elease 20055 $S RDP78B0lPA000100110011-8 hd' I C/PLDS/D/6-7 1 6 11 January 1966 S ? MEMQRN ( Chief, Technical Intel I ige Division ATTENTION: Chief, TAB/Tit) SUBJECTS Additional Pre"wainq and Logic Circuitry for the AP-3 Analytical Plotting System REFERS : I - Contract 1. In accordance with your request, IIpersonnel have been Invited to NPIC on January 25, 1966 to obta n he unclassified information required to enable them to submit a proposal to incorporate a strip photography capability in the AP-3 system. 2. 0 tentatively plans to send three people; one engineer and two programmers. The two programs srs do not hold Agency clearance but since the mathematical model Is unclassified this should not pose it problem. The project eng l neer, holds an Agency Secret clearance. 3. I f appropriate arrangements can be made, It appears that it would be eat, advantageous to set up this meting In the T I D con f erence r o o m . I f at all possible, the consultants that prepared the mathemat i ca l model should be present, as well TiD and IPD personnel as the situation requires. 4. Due to the urgent nature of th i s otter, an early r^ep l y I s requested. Declass Review by NGA. Colonel, USAF Assistant for Plans and Development Distribution: Original and I - Addresses I - Ch/TAB/TID I - Ch/IPD I - Ch/PB/IPD I - Project File/DB (#998125) 1 - Chrono/DB NPIC/P&DS/DB: Approved For Release 2 ~L IfIA-RDP78B04770A000100110011- 25 25X 25X

Includes bibliographies and indexes

Includes bibliographies and indexes

x, 389 p. : 24 cm

We define XPathLog as a Datalog-style extension of XPath. XPathLog provides a clear, declarative language for querying and manipulating XML whose perspectives are especially in XML data integration. In our characterization, the formal semantics is defined wrt. an edge-labeled graph-based model which covers the XML data model. We give a complete, logic-based characterization of XML data and the main language concept for XML, XPath. XPath-Logic extends the XPath language with variable bindings and embeds it into first-order logic. XPathLog is then the Horn fragment of XPath-Logic, providing a Datalog-style, rule-based language for querying and manipulating XML data. The model-theoretic semantics of XPath-Logic serves as the base of XPathLog as a logic-programming language, whereas also an equivalent answer-set semantics for evaluating XPathLog queries is given. In contrast to other approaches, the XPath syntax and semantics is also used for a declarative specification how the database should be updated: when used in rule heads, XPath filters are interpreted as specifications of elements and properties which should be added to the database.

We study the following problem: given a class of logic programs C, determine the maximum number of stable models of a program from C. We establish the maximum for the class of all logic programs with at most n clauses, and for the class of all logic programs of size at most n. We also characterize the programs for which the maxima are attained. We obtain similar results for the class of all disjunctive logic programs with at most n clauses, each of length at most m, and for the class of all disjunctive logic programs of size at most n. Our results on logic programs have direct implication for the design of algorithms to compute stable models. Several such algorithms, similar in spirit to the Davis-Putnam procedure, are described in the paper. Our results imply that there is an algorithm that finds all stable models of a program with n clauses after considering the search space of size O(3^{n/3}) in the worst case. Our results also provide some insights into the question of representability of families of sets as families of stable models of logic programs.