We provide a general investigation of Logic in which the notion of a simple consequence relation is taken to be fundamental. Our notion is more general than the usual one since we give up monotonicity and use multisets rather than sets. We use our notion for characterizing several known logics (including Linear Logic and non-monotonic logics) and for a general, semantics-independent classification of standard connectives via equations on consequence relations (these include Girard's "multiplicatives" and "additives"). We next investigate the standard methods for uniformly representing consequence relations: Hilbert type, Natural Deduction and Gentzen type. The advantages and disadvantages of using each system and what should be taken as good representations in each case (especially from the implementation point of view) are explained. We end by briefly outlining (with examples) some methods for developing non-uniform, but still efficient, representations of consequence relations.

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.

We consider the evolution of information systems towards sophisticated knowledge systems. Investigating the key concepts for information and knowledge systems from a logical point of view, we show that the two most fundamental operations are inference (query answering) and update (`data manipulation'). They have to be available in every system. Advanced information systems may allow for negative, disjunctive and uncertain information. Even more advanced systems (which might be no longer called information, but knowledge systems) will allow for sophisticated reasoning services, such as deductive query answering, active input processing, representing actions, generating explanations, diagnoses and plans. Keywords Knowledge systems, information growth, nonmonotonicity, deduction rules, action rules. 1 Introduction The evolution of information system concepts can be roughly described by the sequence of hierarchical and network databases, relational databases, object-oriented, deductive ...

Heinrich Wansing Dresden University of Technology The knowability paradox is an instance of a remarkable reasoning pattern (actually, a pair of such patterns), in the course of which an occurrence of the possibility operator, the diamond, disappears. In the present paper, it is pointed out how the unwanted disappearance of the diamond may be escaped. The emphasis is not laid on a discussion of the contentious premise of the knowability paradox, namely that all truths are possibly known, but on how from this assumption the conclusion is derived that all truths are, in fact, known. Nevertheless, the solution o#ered is in the spirit of the constructivist attitude usually maintained by defenders of the anti-realist premise. In order to avoid the paradoxical reasoning, a paraconsistent constructive relevant modal epistemic logic with strong negation is defined semantically. The system is axiomatized and shown to be complete.

this paper we look at negation from two different points of view: a syntactical one and a semantical one. Accordingly, we identify two different types of negation. The same connective of a given logic might be of both types, but this might not always be the case. The syntactical point of view is an abstract one. It characterizes connectives according to the internal role they have inside a logic, regardless of any meaning they are intended to have (if any). With regard to negation our main thesis is that the availability of what we call below an internal negation is what makes a logic essentially multiple-conclusion.

An exponential is a unary operator, reminiscent of a modality. We suggest that exponentials be regarded as logic transformers, transforming paraconsistent logics to consistent logics. Consistent logics may appear as certain syntactic subsets of paraconsistent logics. We consider this embedding algebraically and see that an exponential is both a projection and an interior operation. We consider herein a logic constructible duality which is a conservative extension of the paraconsistent version of Nelson's constructible falsity. We give an onto representation theorem for the algebra of constructible duality, show that it provides a model for linear logic and in that model ! is an exponential (as defined by linear logicians) a projection operator and an interior operator. Another exponential ! is definable in constructible duality which has no linear logic counterpart. This is also a projection and an interior operator. Closure and interior operations can be thought of as approximations....

The construction of rational agents is one of the goals that has been pursued in Artificial Intelligence (AI). In most of the architectures that have been proposed for this kind of agents, its behaviour is guided by its set of beliefs. In our work, rational agents are those systems that are permanently engaged in the process of rational inquiry; thus, their beliefs keep evolving in time, as a consequence of their internal inference procedures and their interaction with the environment. Both AI researchers and philosophers are interested in having a formal model of this process, and this is the main topic in our work. Beliefs have been formally modelled in the last decades using doxastic logics. The possible worlds model and its associated Kripke semantics provide an intuitive semantics for these logics, but they seem to commit us to model agents that are logically omniscient and perfect reasoners. We avoid these problems by replacing possible worlds by conceivable situations, which ar...

We begin by motivating the use of paraconsistency and the detection of contradiction supported conclusions by recourse to examples. Next we overview WFSX p and present its embedding into WFS. We then address the problem of detecting contradiction support and relate it to WFSX p's intrinsic properties. Afterwards, we show how to implement two recent modal contradiction related constructs in the language of extended logic programs in order to gain explicit control of contradiction propagation. We finish by making comparisons and drawing some conclusions.

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This paper motivates a comprehensive methodological framework for dealing with some aspects of real-world complexity in information system analysis and design. By complex application problem, we mean a problem that cannot be solved by the current technology in the way that it is perceived and analyzed by application domain specialists. The paper focuses on a motivating case study, the analysis of constraint violations in database management at the Belgian agency for social security. We then re-interpret practices and their problems in terms of current information system technology. Recommendations are derived both for suitable developments of the technology, that would allow a better treatment of complex real-world problems, and for methodological improvements in data management practices in the application domain, that would take better advantage of the current technology.