A principled framework for modular web rule bases and its semantics

We present a principled framework for modular web rule bases, called MWeb. According to this framework, each predicate defined in a rule base is characterized by its defining reasoning mode, scope, and exporting rule base list. Each predicate used in a rule base is characterized by its requesting reasoning mode and importing rule base list. For valid MWeb modular rule bases S, theMWebAS andMWebWFS semantics of each rule base s ∈ S w.r.t. S are defined, model-theoretically. These semantics extend the answer set semantics (AS) and the well-founded semantics with explicit negation (WFSX) on ELPs, respectively, keeping all of their semantical and computational characteristics. Our framework supports: (i) local semantics and different points of view, (ii) local closed-world and open-world assumptions, (iii) scoped negation-as-failure, and (iv) restricted propagation of local inconsistencies. Additionally, it guarantees monotonicity of reasoning, in the case that new rule bases are added to the modular rule base, while the importing rule base list of the predicates of the old rule bases remains the same

Gasping for AIR Why we need Linked Rules and Justifications on the Semantic Web

The Semantic Web is a distributed model for publishing, utilizing and extending structured information using Web protocols. One of the main goals of this technology is to automate the retrieval and integration of data and to enable the inference of interesting results. This automation requires logics and rule languages that make inferences, choose courses of action, and answer questions. The openness of the Web, however, leads to several issues including the handling of inconsistencies, integration of diverse information, and the determination of the quality and trustworthiness of the data. AIR is a Semantic Web-based rule language that provides this functionality while focusing on generating and tracking explanations for its inferences and actions as well as conforming to Linked Data principles. AIR supports Linked Rules, which allow rules to be combined, re-used and extended in a manner similar to Linked Data. Additionally, AIR explanations themselves are Semantic Web data so they can be used for further reasoning. In this paper we present an overview of AIR, discuss its potential as a Web rule language by providing examples of how its features can be leveraged for different inference requirements, and describe how justifications are represented and generated.This material is based upon work supported by the National Science Foundation under Award No. CNS-0831442, by the Air Force Office of Scientific Research under Award No. FA9550-09-1-0152, and by Intelligence Advanced Research Projects Activity under Award No. FA8750-07-2-0031

Modular Nonmonotonic Logic Programming Revisited

Abstract. Recently, enabling modularity aspects in Answer Set Programming (ASP) has gained increasing interest to ease the composition of program parts to an overall program. In this paper, we focus on modular nonmonotonic logic programs (MLP) under the answer set semantics, whose modules may have contextually de-pendent input provided by other modules. Moreover, (mutually) recursive module calls are allowed. We define a model-theoretic semantics for this extended setting, show that many desired properties of ordinary logic programming generalize to our modular ASP, and determine the computational complexity of the new formalism. We investigate the relationship of modular programs to disjunctive logic programs with well-defined input/output interface (DLP-functions) and show that they can be embedded into MLPs

Constraint-based semantics

Montague\u27s famous characterization of the homomorphic relation between syntax and semantics naturally gives way in computational applications to CONSTRAINT-BASED formulations. This was originally motivated by the close harmony it provides with syntax, which is universally processed in a constraint-based fashion. Employing the same processing discipline in syntax and semantics allows that their processing (and indeed other processing) can be as tightly coupled as one wishes - indeed, there needn\u27t be any fundamental distinction between them at all. In this paper, we point out several advantages of the constraint-based view of semantics processing over standard views. These include (i) the opportunity to incorporate nonsyntactic constraints on semantics, such as those arising from phonology and context; (ii) the opportunity to formulate principles which generalize over syntax and semantics, such as those found in HEAD-DRIVEN PHRASE STRUCTURE GRAMMAR; (iii) a characterization of semantic ambiguity, which in turn provides a framework in which to describe disambiguation, and (iv) the opportunity to underspecify meanings in a way difficult to reconcile with other views. The last point is illustrated with an application to scope ambiguity in which a scheme is developed which underspecifies scope but eschews auxiliary levels of logical form