# Prof. Dr. Areski Nait Abdallah's research while affiliated with The University of Western Ontario and other places

## Publications (22)

The tableaux for the propositional logic connectives are inherited from the propositional case (see Sect. 2.2). For the equality rules and the rules for first-order quantifiers one has the following.

The semantics of ionic formulae of rank 0 was discussed in the chapter on partial propositional logic. We now examine the tools necessary for giving the semantics of ionic formulae of rank 1. Valuations are generalized to interpretations capable of dealing with these formulae. The new interpretations are called ionic interpretations of rank 1.

The issue of reasoning with(in) contexts is a fundamental one in logic (cf. e.g. [85] p. 139). It is also relevant in computer science, where it takes many forms: modularisation of logic programs [67, 68], higher-order logic programming [69], multi-agent reasoning [70, 73], formalisation of the logic of scientific discovery [71], algorithmic repres...

As already seen earlier in Chap. 3, partial information ionic logic allows arbitrary nesting of partial information ionic formulae. In other words, the default height and the rank of a given formula can be arbitrarily large.

From the point of view of ionic logic, it is remarkable that what has been swept under the rug in the “non-monotonic” approach is precisely one of the central concepts, if not the central concept, for reasoning with partial information: namely what are justifications, and under which circumstances are they deemed to be acceptable?

The formal proof theory of ionic logic will not be covered in this book. Only an outline, with some motivations, are given here. Intuitively, the general question addressed here is: what is the role (or the impact) of “semantic gaps” at the proof-theoretic level?

It has been shown in Lemmata 8.1.8 and 8.1.9 that the inference rules of the naive axiomatization of propositional partial information ionic logic are sound in the sense that they “split” into several weaker inference rules that are sound. The soundness of I-modus ponens was examined in the chapter on partial propositional logic.

This chapter discusses the “Lakatosian” aspect of ionic logic, i.e. the structuring of knowledge into kernel, justification and belt knowledge. Recall that Chap. 2 discussed the purely partial aspect of the logic. Thus one has two layers of complexity in PIL, a partial propositional logic layer presented in Chap. 2, and a tentative reasoning with p...

The question examined in this chapter is the following: Along which extremum path will (or did) a logic system evolve and reach a state where the currently observed facts are true (in a soft sense)? This question arises in particular when one attempts to find some temporal explanation to some observed phenomenon. The tool used for solving this ques...

Let us reconsider the Tweety example: Tweety is a bird. Birds typically fly. In this example, query: Does Tweety fly? should fail, because it asks whether some kernel knowledge is present, and that knowledge is simply not there. However, a weaker question may be asked: Is there any justification such that Tweety flies under that justification? This...

What differentiates reasoning with total information from reasoning with partial information is that, in the latter case, a certain amount of tentative reasoning has to be made. We adopt here a logical approach to tentative reasoning. In this approach, a given tentative conclusion will not be qualified by some probability (as in probabilistic reaso...

If we consider a partial information logic program as being simply a finite set of partial information ionic formulae, then we can consider its class of models

We now define a reasoning system with axioms and inference rules for first-order logic with partial information ions.

In this chapter, several applications of Beth tableaux and of the fundamental principle of the statics of logic systems to a variety of problems are discussed.

In this section, we generalize partial information ionic logic from propositional to first-order logic. Syntax and semantics are discussed first. The algebraic properties of the logic are then examined in the next chapter.

In this chapter, we apply the techniques introduced in the previous chapter, and proceed to show that the least action principle is sufficient for solving several other instances of the frame problem.

We now discuss the model theory of (classical) first-order logic together with partial interpretations. As in the propositional case, the syntax of partial firstorder logic is essentially the same as in the classical case. The main difference from classical first-order logic is the model theory, and the resulting formal axiomatics. The reader is re...

This chapter presents an analytical proof procedure for partial information ionic logic.

In this section, we examine the model theory and proof theory of propositional logic with partial interpretations. The syntax of partial propositional logic is essentially the same as in the classical case, and is briefly reviewed. The main difference will be the model theory. As a result, the axiomatics will be affected by the new semantic point o...

In the previous chapters, a new kind of logical statement (partial information ions) has been introduced, and its semantics defined. One has also given a method for reasoning with these new objects by means of Beth tableaux. The question we now address is the following: how does one build proofs, using axioms and inference rules, with these new sta...

It is widely believed that reasoning is a manifestation of intelligence, and many computer science scholars have claimed, that, by definition, Artificial Intelligence requires programs with a capacity to “reason.” The precise meaning and scope of such a claim is an epistemological and philosophical issue that shall not be discussed here, and the de...

The motivation behind the development of non-monotonic reasoning was to formalize the notion of “jumping to conclusions,” and thus solve the frame problem. Unfortunately, Hanks and McDermott [28] showed that McCarthy’s circumscription and Reiter’s default logic yield unwanted results for the Yale shooting problem: they both yield a model where the...