Characterizing and Extending Answer Set Semantics using Possibility Theory

Answer Set Programming (ASP) is a popular framework for modeling combinatorial problems. However, ASP cannot easily be used for reasoning about uncertain information. Possibilistic ASP (PASP) is an extension of ASP that combines possibilistic logic and ASP. In PASP a weight is associated with each rule, where this weight is interpreted as the certainty with which the conclusion can be established when the body is known to hold. As such, it allows us to model and reason about uncertain information in an intuitive way. In this paper we present new semantics for PASP, in which rules are interpreted as constraints on possibility distributions. Special models of these constraints are then identified as possibilistic answer sets. In addition, since ASP is a special case of PASP in which all the rules are entirely certain, we obtain a new characterization of ASP in terms of constraints on possibility distributions. This allows us to uncover a new form of disjunction, called weak disjunction, that has not been previously considered in the literature. In addition to introducing and motivating the semantics of weak disjunction, we also pinpoint its computational complexity. In particular, while the complexity of most reasoning tasks coincides with standard disjunctive ASP, we find that brave reasoning for programs with weak disjunctions is easier.Comment: 39 pages and 16 pages appendix with proofs. This article has been accepted for publication in Theory and Practice of Logic Programming, Copyright Cambridge University Pres

Epistemic NP Modifiers

The paper considers participles such as "unknown", "identified" and "unspecified", which in sentences such as "Solange is staying in an unknown hotel" have readings equivalent to an indirect question "Solange is staying in a hotel, and it is not known which hotel it is." We discuss phenomena including disambiguation of quantifier scope and a restriction on the set of determiners which allow the reading in question. Epistemic modifiers are analyzed in a DRT framework with file (information state) discourse referents. The proposed semantics uses a predication on files and discourse referents which is related to recent developments in dynamic modal predicate calculus. It is argued that a compositional DRT semantics must employ a semantic type of discourse referents, as opposed to just a type of individuals. A connection is developed between the scope effects of epistemic modifiers and the scope-disambiguating effect of "a certain".Comment: Final pre-publication version, 27 pages, Postscript. Final version appears in the proceedings of SALT VI

Logical Reduction of Metarules

International audienceMany forms of inductive logic programming (ILP) use metarules, second-order Horn clauses, to define the structure of learnable programs and thus the hypothesis space. Deciding which metarules to use for a given learning task is a major open problem and is a trade-off between efficiency and expressivity: the hypothesis space grows given more metarules, so we wish to use fewer metarules, but if we use too few metarules then we lose expressivity. In this paper, we study whether fragments of metarules can be logically reduced to minimal finite subsets. We consider two traditional forms of logical reduction: subsumption and entailment. We also consider a new reduction technique called derivation reduction, which is based on SLD-resolution. We compute reduced sets of metarules for fragments relevant to ILP and theoretically show whether these reduced sets are reductions for more general infinite fragments. We experimentally compare learning with reduced sets of metarules on three domains: Michalski trains, string transformations, and game rules. In general, derivation reduced sets of metarules outperform subsumption and entailment reduced sets, both in terms of predictive accuracies and learning times

Exclamative clauses at the syntax-semantics interface

Exclamative clauses exhibit a structural diversity which raises the question of whether they form a clause type in the sense of Sadock & Zwicky (1985). Based on data from English, Italian, and Paduan, we argue that the class of exclamatives is syntactically characterizable in terms of a pair of abstract syntactic properties. Moreover, we propose that these properties encode two components of meaning which uniquely define the semantics and pragmatics of exclarnatives. Overall, our paper is a contribution to the study of the syntaxlsemantics interface and offers a new perspective on the notion of clause type

The search for truth: Appositives weigh in

The semantic and pragmatic contribution of appositives to their containing sentence is a subject of continuing debate. While unidimensional semantic accounts propose that appositives contribute their truth conditions to their containing sentence, multidimensional accounts predict that they do not. In three experiments, we directly compared judgments of the truth of sentences containing appositives and sentences containing conjunctions. Our findings contribute both a methodological and a theoretical point. First, we show that no conclusions about the truth-conditional contributions of appositives can be drawn from experimental work without further investigation of how participants provide truth value judgments for complex sentences. Second, we show that while appositives appear to contribute truth values to their containing sentences, participants are highly sensitive to task features when they compute the truth value of sentences with appositives and also, crucially, with conjunctions. Specifically, we show that both sentences containing appositives and those containing conjunctions can be judged true even when the appositive or one conjunct is patently false. We conclude that it is unlikely that these results reflect semantic judgments, and suggest that they reflect truth only at the speech-act level

Non-clausal multi-ary alpha-generalized resolution calculus for a finite lattice-valued logic

Due to the need of the logical foundation for uncertain information processing, development of efficient automated reasoning system based on non-classical logics is always an active research area. The present paper focuses on the resolution-based automated reasoning theory in a many-valued logic with truth-values defined in a lattice-ordered many-valued algebraic structure - lattice implication algebras (LIA). Specifically, as a continuation and extension of the established work on binary resolution at a certain truth-value level α (called α-resolution), a non-clausal multi-ary α-generalized resolution calculus is introduced for a lattice-valued propositional logic LP(X) based on LIA, which is essentially a non-clausal generalized resolution avoiding reduction to normal clausal form. The new resolution calculus in LP(X) is then proved to be sound and complete. The concepts and theoretical results are further extended and established in the corresponding lattice-valued first-order logic LF(X) based on LIA