Properties and modeling of partial conjunction/disjunction

AI Communications, 2011

In this paper we consider a logical treatment for the ordered disjunction operator × introduced by Brewka, Niemelä and Syrjänen in their Logic Programs with Ordered Disjunctions (LPOD). LPODs are used to represent preferences in logic programming under the answer set semantics. Their semantics is defined by first translating the LPOD into a set of normal programs (called split programs) and then imposing a preference relation among the answer sets of these split programs. We concentrate on the first step and show how a suitable translation of the ordered disjunction as a derived operator into the logic of Here-and-There allows capturing the answer sets of the split programs in a direct way. We use this characterisation not only for providing an alternative implementation for LPODs, but also for checking several properties (under strongly equivalent transformations) of the × operator, like for instance, its distributivity with respect to conjunction or regular disjunction. We also make a comparison to an extension proposed by Kärger, Lopes, Olmedilla and Polleres, that combines × with regular disjunction.

In this paper, we develop a method to find the uncertain consequent by fusing the uncertain antecedent and the uncertain implication rule. In particular with Dempster-Shafer theoretic models utilized to capture the uncertainty intervals associated with the antecedent and the rule itself, we derive bounds on the confidence interval associated with the rule consequent. We derive inequalities for the belief and plausibility values of the consequent and with least commitment choice they become equations. We also demonstrate the consistency of our model with probability and classical logic.

In this paper, I sketch an account of the (historical) philosophy of indicator semantics and its attempt to provide for mental content. I conclude that indicator semantics fell out of favor from the literature because it necessitated disjunctive mental content. From this shortcoming, I turn my analysis to teleosemantics, a contemporary account of mental content. I argue that teleosemantics is only capable of producing generalized representational mental states, a conclusion no better than the disjunctive content entailed by indicator semantics.

2006

In this work we present a backjumping technique for Disjunctive Logic Programming under the Stable Model Semantics (SDLP). It builds upon related techniques that had originally been introduced for constraint solving, which have been adapted to propositional satisfiability testing, and recently also to non-disjunctive logic programming under the stable model semantics (SLP) [1, 2]. We focus on backjumping without clause learning, providing a new theoretical framework for backjumping in SDLP, elaborating on and exploiting peculiarities of the disjunctive setting. We present a reason calculus and associated computations, which -compared to the traditional approaches -reduces the information to be stored, while fully preserving the correctness and the efficiency of the backjumping technique, handling specific aspects of disjunction in a benign way. We implemented the proposed technique in DLV, the state-ofthe-art SDLP system. We have conducted several experiments on hard random and structured instances in order to assess the impact of backjumping, using DLV with and without the backjumping method described in this paper, using as a parameter to both two different heuristic functions. Our conclusion is that under any of the heuristic functions, DLV with backjumping is favourable to DLV without backjumping. DLV with backjumping performs particularly well on structured satisfiability and quantified boolean formula instances, where the search space and execution time are effectively cut.

Proceedings of the 13th conference on Computational linguistics -, 1990

\Ve introduce lea.tare terms containing sorts, vztriables, negation and named disjunction for the specification of feature structures. We show that the possibility to label di@mctions with names has m~tjor advantages both for the 'use of feature logic in computationaJ linguistics and its implementation. We give an open world semantics for feature terms, where the denotation of a term is determined in dependence on the disjunctive conte:rt, i.e. the choices taken for the disjunctions. We define conte:ct-unique feature description.% a relational, constraint-based rcpresentation language and give a normMization procedure that allows to test consistency of feature terms. This procedure does not only avoid expansion 1o disjunctive normal fbrm but maintains also structure sharing between information contained in dii:ferent disjuncts as much as possible. Context-unique feature descriptions can be easily implemented in environments that support ordinary unification (such as I?UOLOG).

Logic Programming with Annotated Disjunctions (LPADs) is a formalism for modeling probabilistic information that has recently received increased attention. The LPAD semantics, while being simple and clear, suffers from the requirement of having function free-programs, which is a strong limitation. In this paper we present an extension of the semantics that removes this restriction and allows us to write programs modeling infinite domains, such as Hidden Markov Models. We show that the semantics is well-defined for a large class of programs. Moreover, we present the algorithm "Probabilistic Inference with Tabling and Answer subsumption" (PITA) for computing the probability of queries to programs according to the extended semantics. Tabling and answer subsumption not only ensure the correctness of the algorithm with respect to the semantics but also make it very efficient on programs without function symbols. PITA has been implemented in XSB and tested on six domains: two with function symbols and four without. The execution times are compared with those of ProbLog, cplint and CVE. PITA was almost always able to solve larger problems in a shorter time on both type of domains.

2000

At present, the search for specific information on the World Wide Web is faced with several problems, which arise on the one hand from the vast number of information sources available, and on the other hand from their intrinsic heterogeneity, since standards are missing. A promising approach for solving the complex problems emerging in this context is the use of multi-agent systems of information agents, which cooperatively solve advanced information-retrieval problems. This requires advanced capabilities to address complex tasks, such as search and assessment of information sources, query planning, information merging and fusion, dealing with incomplete information, and handling of inconsistency. In this paper, our interest lies in the role which some methods from the field of declarative logic programming can play in the realization of reasoning capabilities for information agents. In particular, we are interested to see in how they can be used, extended, and further developed for the specific needs of this application domain. We review some existing systems and current projects, which typically address information-integration problems. We then focus on declarative knowledge-representation methods, and review and evaluate approaches and methods from logic programming and nonmonotonic reasoning for information agents. We discuss advantages and drawbacks, and point out the possible extensions and open issues. Contents 1 Introduction 3 2 Intelligent Information Agents 4 3 Problems and Challenges 8 4 Systems and Frameworks 9 4.1 Cohen's Information System for Structured Collections of Text 10 4.2 Information Manifold 11 4.3 Carnot 11 4.4 InfoSleuth 12 4.5 Infomaster 12 4.6 COIN 13 7 Revision and Update 7.1 Revision Programs by Marek and Truszczyński 7.2 Update Rules as Logic Programs by Pereira et al. 7.3 Abductive Updates by Inoue and Sakama 7.4 Updates by Means of PLPs by Foo and Zhang 7.5 Dynamic Logic Programming by Alferes et al. 7.6 Updates and Preferences by Alferes and Pereira 7.7 Inheritance Programs and Updates 7.8 Revision of Preference Default Theories by Brewka 7.9 Arbitration 8 Quantitative Information 8.1 Disjunctive Programs with Weak Constraints by Buccafurri et al. 8.2 Weight Constraint Rules by Niemelä et al. 8.3 Weighted Logic Programming by Marek and Truszczyński 8.4 Probabilistic Programs by Subrahmanian et al. 9 Temporal Reasoning 9.1 Reasoning about Actions 9.2 Temporal Logics for BDI agents 9.3 LUPS, a Language for Specifying Updates 10 Evaluation 10.1 Preference Handling 10.2 Logic Programs with Quantitative Information 10.3 Revision and Update 10.4 Temporal Reasoning 11 Conclusion References

Mediterranean Journal of Mathematics, 2007

In many practical applications of fuzzy logic it seems clear that one needs more flexibility in the choice of the conjunction: in particular, the associativity and the commutativity of a conjunction may be removed. Motivated by these considerations, we present several classes of conjunctors, i.e. binary operations on [0, 1] that are used to extend the boolean conjunction from {0, 1} to [0, 1], and characterize their respective residual implicators. We establish hence a one-to-one correspondence between construction methods for conjunctors and construction methods for residual implicators. Moreover, we introduce some construction methods directly in the class of residual implicators, and, by using a deresiduation procedure, we obtain new conjunctors.

Journal of Logic and Computation, 2012

When combining logics while imposing the sharing of connectives, the result is frequently inconsistent. In fact, in fibring, fusion and other forms of combination reported in the literature, each shared connective inherits the logical properties of each of its components. A new form of combining logics (meet-combination) is proposed where such a connective inherits only the common logical properties of its components. The conservative nature of the proposed combination is shown to hold without provisos. Preservation of soundness and completeness is also proved. Illustrations are provided involving classical, intuitionistic and modal logics.

Proceedings of the twenty-second ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems - PODS '03, 2003

Under either the or-semantics or the weak semantics, the answer to a query over semistructured data consists of maximal rather than complete matchings, i.e., some query variables may be assigned null values. In the relational model, a similar effect is achieved by computing the full disjunction (rather than the natural join or equijoin) of the given relations. It is shown that under either the or-semantics or the weak semantics, query evaluation has a polynomial-time complexity in the size of the query, the database and the result. It is also shown that the evaluation of full disjunctions is reducible to query evaluation under the weak semantics and hence can be done in polynomial time in the size of the input and the output. Complexity results are also given for two related problems. One is evaluating a projection of the full disjunction and the other is evaluating the set of all tuples in the full disjunction that are non-null on some given attributes. In the special case of γ-acyclic relation schemes, both problems have polynomial-time algorithms in the size of the input and the output. In the general case, such algorithms do not exist, assuming that P = NP. Finally, it is shown that the weak semantics can generalize full disjunctions by allowing tuples to be joined according to general types of conditions, rather than just equalities among attributes. proposed full disjunctions, which are commutative and associative, as an alternative to outerjoins. Essentially, the full disjunction of a set of relations is obtained by taking all joins of any subset of relations, excluding joins that involve a Cartesian product, and removing subsumed tuples. Rajaraman and Ullman [23] enunciated full disjunctions as a mechanism for integrating information from the Web, since the user cannot have any a priori knowledge of where information might be incomplete.