Annotated logics were introduced in [43] and later studied in [5, 7, 31, 32]. In [31], annotations were extended to allow variables and functions, and it was argued that such logics can be used to provide a formal semantics for rule-based expert systems with uncertainty. In this paper we continue to investigate the power of this approach. First, we introduce a new semantics for such programs based on ideals of lattices. Subsequently, some proposals for multivalued logic programming [5, 7, 32, 47, 40, 18] as well as some formalisms for temporal reasoning [1, 3, 42] are shown to fit into this framework. As an interesting by-product of this investigation, we obtain a new result concerning multivalued logic programming: a model theory for Fitting's bilattice-based logic programming, which until now has not been characterized model-theoretically. This is accompanied by a corresponding proof theory. 1 Introduction Large knowledge bases can be inconsistent in many ways. Nevertheless, certain...

Of all scientific investigations into reasoning with uncertainty and chance, probability theory is perhaps the best understood paradigm. Nevertheless, all studies conducted thus far into the semantics of quantitative logic programming (cf. van Emden [51], Fitting [18, 19, 20], Blair and Subrahmanian [5, 6, 49, 50], Kifer et al [29, 30, 31]) have restricted themselves to non-probabilistic semantical characterizations. In this paper, we take a few steps towards rectifying this situation. We define a logic programming language that is syntactically similar to the annotated logics of [5, 6], but in which the truth values are interpreted probabilistically. A probabilistic model theory and fixpoint theory is developed for such programs. This probabilistic model theory satisfies the requirements proposed by Fenstad [16] for a function to be called probabilistic. The logical treatment of probabilities is complicated by two facts: first, that the connectives cannot be interpreted truth function...

This paper presents declarative semantics of possibly inconsistent disjunctive logic programs. We introduce the paraconsistent minimal and stable model semantics for extended disjunctive programs, which can distinguish inconsistent information from others in a program. These semantics are based on lattice-structured multi-valued logics, and are characterized by a new fixpoint semantics of extended disjunctive programs. Applications of the paraconsistent semantics for reasoning in inconsistent programs are also presented. Keywords: Extended disjunctive programs, inconsistency, multi-valued logic, paraconsistent stable model semantics. 3 Journal of Logic and Computation 5: 265-285, Oxford University Press, 1995. 1 1

In this chapter we motivate the use of paraconsistency, and survey the most salient paraconsistent semantics for (extended) logic programs, which are briefly defined and explained. Most of the semantics are accompanied with their multi-valued model theory, giving them a new perspective. The survey also presents new results regarding the embedding of part of these semantics into normal logic programs under Well-Founded Semantics [20], Partial Stable Model Semantics (or stationary semantics) [48], and Stable Model Semantics [21]. Furthermore, a concise recapitulation of other related paraconsistent formalisms is made. The reader is assumed to have a good knowledge of the semantics of normal logic programs. We believe a comprehensive coverage of the topic as it stands at present is attained here.

Deductive databases result from the integration of relational database and logic programming techniques. However, significant problems remain inherent in this simple synthesis from the language point of view. In this paper, we discuss these problems from four different aspects: complex values, object orientation, higherorderness, and updates. In each case, we examine four typical languages that address the corresponding issues.

This paper presents a declarative semantics of logic programs which possibly contain inconsistent information. We introduce a multi-valued interpretation of logic programs and present the extended well-founded semantics for paraconsistent logic programs. In this setting, a meaningful information is still available in the presence of an inconsistent information in a program and any fact which is affected by an inconsistent information is distinguished from the others. The well-founded semantics is also extended to disjunctive paraconsistent logic programs. 1 Introduction Recent studies have greatly enriched an expressive power of logic programming as a tool for knowledge representation. Handling classical negation as well as negation by failure in a program is one of such extension. An extended logic program, which is introduced by Gelfond and Lifschitz [GL90], distinguishes two types of negation and enables us to deal with explicit negation as well as default negation in a pro...

We present a generalisation of the relational data model based on a 4-valued paraconsistent logic. Our data model is capable of manipulating incomplete as well as inconsistent information. For this model, we define algebraic operators that are generalisations of the usual operators, such as union, selection, join, on ordinary relations. Our data model can underlie any database management system that deals with incomplete or inconsistent information. As another application of our model and its algebra, we present a bottomup method for constructing the weak well-founded model of general deductive databases. This method can be very simply extended to construct the well-founded model.

Integrating knowledge from multiple sources is an important aspect of automated reasoning systems. In the first part of this series of papers, we presented a uniform declarative framework, based on annotated logics, for amalgamating multiple knowledge bases when these knowledge bases (possibly) contain inconsistencies, uncertainties, and non-monotonic modes of negation. We showed that annotated logics may be used, with some modifications, to mediate between different knowledge bases. The multiple knowledge bases are amalgamated by embedding the individual knowledge bases into a lattice. In this paper, we briefly describe an SLD-resolution based proof procedure that is sound and complete w.r.t. our declarative semantics. We will then develop an OLDT-resolution based query processing procedure, MULTI OLDT, that satisfies two important properties: (1) efficient reuse of previous computations is achieved by maintaining a table -- we describe the structure of this table and show that table...

Uncertainty, incompleteness and vagueness are typical features of common-sense as well as expert knowledge. Reasoning based on such knowledge demands strategies to combine divergent information. All the more this is true in the context of integrating knowledge bases. This paper addresses knowledge representation, reasoning, and conflict management with many-valued logics. We show by some examples how information can be expressed in many-valued Horn clauses, how fitting truth value spaces can be found-in this context we also consider bilatticesand how conflict solving strategies can be involved. We do not focus on technical details but try to open up prospects of applications.

Abstract The use of agents in today’s Internet world is expanding rapidly. Yet, agent developers proceed largely under the optimistic assumption that agents will be error-free. Errors may arise in agents for numerous reasons — agents may share a workspace with other agents or humans and updates made by these other entities may cause an agent to face a situation that it was not explicitly programmed to deal with. Likewise, errors in coding agents may lead to inconsistent situations where it is unclear how the agent should act. In this paper, we define an agent execution model that allows agents to continuing acting “reasonably ” even when some errors of the above types occur. More importantly, in our framework, agents take “repair ” actions automatically when confronted with such situations, but while taking such repair actions, they can often continue to engage in work and/or interactions with other agents that are unaffected by repairs. 1