The Experts below are selected from a list of 2685 Experts worldwide ranked by ideXlab platform

Luigi Palopoli - One of the best experts on this subject based on the ideXlab platform.

  • On the tractability of minimal model computation for some CNF theories
    Artificial Intelligence, 2014
    Co-Authors: Fabrizio Angiulli, Rachel Ben-eliyahu-zohary, Fabio Fassetti, Luigi Palopoli
    Abstract:

    Designing algorithms capable of efficiently constructing minimal models of Conjunctive Normal Form theories (CNFs) is an important task in AI. This paper provides new results along this research line and presents new algorithms for performing minimal model finding and checking over Positive propositional CNFs and model minimization over propositional CNFs. A CNF is Positive if each of its clauses has at least a Positive Literal. An algorithmic schema, called the Generalized Elimination Algorithm (GEA) is presented, that computes a minimal model of any Positive CNF. The schema generalizes the Elimination Algorithm (EA) [5], which computes a minimal model of Positive head-cycle-free (HCF) CNF theories. While the EA always runs in polynomial time in the size of the input HCF CNF, the complexity of the GEA depends on the complexity of the specific eliminating operator invoked therein, which may in general turn out to be exponential. Therefore, a specific eliminating operator is defined by which the GEA computes, in polynomial time, a minimal model for a class of CNF that strictly includes head-elementary-set-free (HEF) CNF theories [14], which form, in their turn, a strict superset of HCF theories. Furthermore, in order to deal with the high complexity associated with recognizing HEF theories, an ''incomplete'' variant of the GEA (called IGEA) is proposed: the resulting schema, once instantiated with an appropriate elimination operator, always constructs a model of the input CNF, which is guaranteed to be minimal if the input theory is HEF. In the light of the above results, the main contribution of this work is the enlargement of the tractability frontier for the minimal model finding and checking and the model minimization problems.

  • A language for updating logic programs and its implementation
    The Journal of Logic Programming, 1995
    Co-Authors: Nicola Leone, Luigi Palopoli, Massimo Romeo
    Abstract:

    Abstract This paper proposes an update language, called ULL , for knowledge systems based on logic programming. This language is built upon two basic update operators, respectively denoting insertion and deletion of a Positive Literal (atom). Thus, simple control structures are defined for combining the basic updates into programs capable of expressing complex updates. The semantics of the update language is centered around the idea of executing a basic update by directly modifying the truth valuation of that (intensionally or extensionally defined) atom which is the object of the update. This modification propagates recursively to the truth valuations of those atoms dependent upon the updated one. The expressive power of this language is discussed, its implementation is studied, and an interpreter is given, which is proven correct w.r.t. the defined formal semantics. The computational complexity of the proposed implementation is also analyzed, showing that the update language interpreter runs efficiently. Finally, three extensions to ULL are discussed. The first allows the programmer to insert and delete rules, the second supports a form of hypothetical reasoning about updates, and the last introduces facilities in the language for the definition and the calling of update procedures.

  • Modifying Intensional Logic Knowledge
    Fundamenta Informaticae, 1994
    Co-Authors: Nicola Leone, Luigi Palopoli, Massimo Romeo
    Abstract:

    This paper addresses the problem of updating knowledge encoded in the form of a logic program. Our approach is based upon the idea of executing a basic update by directly modifying the truth valuation of the (intensionally or extensionally defined) atom which is the object of an update. The modifications propagate, in a recursive fashion, to the truth valuations of atoms depending on the updated one. An update language is defined around this central idea. The language is built upon two basic update operators, respectively denoting insertion and deletion of a Positive Literal (atom). Several structures are defined for combining basic updates into complex ones and controlling the execution flow.

Stepan G. Margaryan - One of the best experts on this subject based on the ideXlab platform.

  • Necessary and sufficient conditions for Boolean satisfiability.
    arXiv: Computational Complexity, 2019
    Co-Authors: Stepan G. Margaryan
    Abstract:

    The study in this article seeks to find conditions that are necessary and sufficient for the satisfiability of a Boolean function. We will use the concept of special covering of a set introduced in [9] and study the relation of this concept with the satisfiability of Boolean functions. We show that the problem of existence of a special covering of a set is equivalent to the Boolean satisfiability problem. Thus, an important result is the proof of the existence of necessary and sufficient conditions for the existence of special covering of the set. This result allows us to formulate the necessary and sufficient conditions for Boolean satisfiability, considering the function in conjunctive normal form as a set of clauses. To formulate the same result in term of Boolean function we introduce the concept of proportional conjunctive normal form of a function, which is a conjunctive normal form of a function with the condition that each clause contains a negative Literal or each clause contains a Positive Literal. Thus, we obtain that the satisfiability of a Boolean function represented in conjunctive normal form is equivalent to the possibility of converting it into a function in proportional conjunctive normal form by Literal inversion.To prove these results, some algorithmic procedures are used. As a result of these procedures, in parallel, we obtain the Boolean values for the variables that provide the satisfiability of the function.Estimates of the complexity of these algorithmic procedures will be presented in the next article. Generally accepted terminology on set theory, Boolean functions, and graph theory is consistent with the terminology found in the relevant works included in the bibliography [1],[2],[3]. The newly introduced terms are not found in use by other authors and do not contradict to other terms.

Jacques Cohen - One of the best experts on this subject based on the ideXlab platform.

  • logic programming and constraint logic programming
    ACM Computing Surveys, 1996
    Co-Authors: Jacques Cohen
    Abstract:

    Logic programming is a language paradigm based on logic, more specifically on resolution theorem proving in the predicate calculus as proposed in Robinson [1965]. Robinson had the foresight to distinguish the importance of two components in automatic theorem proving: a single inference rule called resolution and the testing for equality of trees called unification. Resolution is an inference step used to prove the validity of predicate calculus formulas expressed as clauses. In its simplest version: P ~ Q and -P ~ R imply Q ~ R, which is called the resolvant. Unification is the matching of terms used in a resolution step. It consists of testing the satisfiability of the equality of terms (i.e., labeled trees) whose leaves may contain variables. For example, the unification of the terms p(X, q(Z, a)) and p(b, q(a, Y)) succeeds, yielding the bindings X 5 b, Z 5 a, and Y 5 a. Prolog, the main representative of LP, consists of a sequence of Horn clauses. A Horn clause is one containing (at most) one Positive Literal. The term definite clause is used to denote a clause with exactly one Positive Literal. Prolog programs can be viewed as a set of definite clauses in which the Positive Literal is the head of the rule and the negative Literals constitute the body or tail of the rule. From a procedural point of view, a head corresponds to the definition of a Boolean function whose body consists of conjunctions of calls to the Boolean functions representing the tail [Kowalski 1979]. A quintessential example of a Prolog program is that of append. It consists of two Horn clauses specifying that list L3 is the concatenation of two lists, L1 and L2:

Fabrizio Angiulli - One of the best experts on this subject based on the ideXlab platform.

  • On the tractability of minimal model computation for some CNF theories
    Artificial Intelligence, 2014
    Co-Authors: Fabrizio Angiulli, Rachel Ben-eliyahu-zohary, Fabio Fassetti, Luigi Palopoli
    Abstract:

    Designing algorithms capable of efficiently constructing minimal models of Conjunctive Normal Form theories (CNFs) is an important task in AI. This paper provides new results along this research line and presents new algorithms for performing minimal model finding and checking over Positive propositional CNFs and model minimization over propositional CNFs. A CNF is Positive if each of its clauses has at least a Positive Literal. An algorithmic schema, called the Generalized Elimination Algorithm (GEA) is presented, that computes a minimal model of any Positive CNF. The schema generalizes the Elimination Algorithm (EA) [5], which computes a minimal model of Positive head-cycle-free (HCF) CNF theories. While the EA always runs in polynomial time in the size of the input HCF CNF, the complexity of the GEA depends on the complexity of the specific eliminating operator invoked therein, which may in general turn out to be exponential. Therefore, a specific eliminating operator is defined by which the GEA computes, in polynomial time, a minimal model for a class of CNF that strictly includes head-elementary-set-free (HEF) CNF theories [14], which form, in their turn, a strict superset of HCF theories. Furthermore, in order to deal with the high complexity associated with recognizing HEF theories, an ''incomplete'' variant of the GEA (called IGEA) is proposed: the resulting schema, once instantiated with an appropriate elimination operator, always constructs a model of the input CNF, which is guaranteed to be minimal if the input theory is HEF. In the light of the above results, the main contribution of this work is the enlargement of the tractability frontier for the minimal model finding and checking and the model minimization problems.

Ken Satoh - One of the best experts on this subject based on the ideXlab platform.

  • computing minimal models by Positively minimal disjuncts
    International Symposium on Artificial Intelligence, 2009
    Co-Authors: Ken Satoh
    Abstract:

    In this paper, we consider a method of computing minimal models in propositional logic. We firstly show that Positively minimal disjuncts in DNF (Disjunctive Normal Form) of the original axiom corresponds with minimal models. A disjunct D is Positively minimal if there is no disjunct which contains less Positive Literal than D. We show that using superset query and membership query which were used in some learning algorithms in computational learning theory, we can compute all the minimal models. We then give a restriction and an extension of the method. The restriction is to consider a class of Positive (sometimes called monotone) formula where minimization corresponds with diagnosis and other important problems in computer science. Then, we can replace superset query with sampling to give an approximation method. The algorithm itself has been already proposed by [Valiant84], but we show that the algorithm can be used to approximate a set of minimal models as well. On the other hand, the extension is to consider circumscription with varied propositions. We show that we can compute equivalent formula of circumscription using a similar technique to the above.

  • JSAI-isAI Workshops - Computing minimal models by Positively minimal disjuncts
    New Frontiers in Artificial Intelligence, 2009
    Co-Authors: Ken Satoh
    Abstract:

    In this paper, we consider a method of computing minimal models in propositional logic. We firstly show that Positively minimal disjuncts in DNF (Disjunctive Normal Form) of the original axiom corresponds with minimal models. A disjunct D is Positively minimal if there is no disjunct which contains less Positive Literal than D. We show that using superset query and membership query which were used in some learning algorithms in computational learning theory, we can compute all the minimal models. We then give a restriction and an extension of the method. The restriction is to consider a class of Positive (sometimes called monotone) formula where minimization corresponds with diagnosis and other important problems in computer science. Then, we can replace superset query with sampling to give an approximation method. The algorithm itself has been already proposed by [Valiant84], but we show that the algorithm can be used to approximate a set of minimal models as well. On the other hand, the extension is to consider circumscription with varied propositions. We show that we can compute equivalent formula of circumscription using a similar technique to the above.