In this paper we discuss the logical and commonsense intuitions behind the concept of generic object and the possibility of characterizing this concept by means of both classical rst{order logic and circumscription. We also show that circumscription can be used in the characterization of the concept of generic point of a curve, as it appears in algebraic geometry. Finally, we show that several ...

In this paper, we extend defeasible logic (a computationally-oriented non-monotonic logic) in order to deal with temporalised rules. In particular, we extend the logic to cope with durative facts, as well as with delays between the antecedent and the consequent of rules. We showed that the extended temporalised framework is suitable to model different types of causal relations which have been i...

Frame systems—the ancestors of Description Logics—supported a form of defeasible inheritance and overriding. Such nonmonotonic features disappeared from implementations after the logical reconstruction of frame systems, although applications provide interesting use cases for nonmonotonic inferences. This talk gives an overview of the nonmonotonic DLs introduced so far, and illustrates the many ...

Extension-based argumentation semantics is a successful approach for performing non-monotonic reasoning based on argumentation theory. An interesting property of some extension-based argumentation semantics is that these semantics can be characterized in terms of logic programming semantics. In this paper, we present novel results in this topic. In particular, we show that one can induce an arg...

Contextual logic CoL is specified through an inference system which takes into account the context of reasoning, i.e. all given facts whatsoever. That is to say, conclusions are inferred with respect to the full set of premises. Hence, statements are relative to a context and they are expressed by means of formulas indexed with sets of formulas. A modal extension ECoL is also proposed for which...

Iffy oughts figure prominently in a variety of paradoxes of deontic logic. A satisfying response to these paradoxes is a non-negotiable component of any adequate semantic story about conditionals and deontic modals. I demonstrate that such a story can be told but doing so requires that we supplement a semantics that pays proper attention to the sensitivity of ifs and oughts to contextual inform...

Consistency-based approaches in nonmonotonic reasoning may be expected to yield multiple sets of default conclusions for a given default theory. Reasoning about such extensions is carried out at the meta-level. In this paper, we show how such reasoning may be carried out at the object level for a large class of default theories. Essentially we show how one can translate a (normal) default theor...

The second postulate of Katsuno and Mendelzon characterizes irrelevant updates. We show that the postulate has to be modified, if nonmonotonic assumptions are considered. Our characterization of irrelevant updates is based on a dependency framework, which provides an alternative semantics of multidimensional dynamic logic programming.

This paper has two goals. First, we develop frameworks for logical systems which are able to reflect not only nonmonotonic patterns of reasoning, but also paraconsistent reasoning. Our second goal is to have a better understanding of the conditions that a useful relation for nonmonotonic reasoning should satisfy. For this we consider a sequence of generalizations of the pioneering works of Gabb...