There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

An Introduction to MultiAgent Systems.

Publisher Summary This chapter discusses the mathematical theory of computation. Computation essentially explores how machines can be made to carry out intellectual processes. Any intellectual process that can be carried out mechanically can be performed by a general purpose digital computer. There are three established directions of mathematical research that are relevant to the science of computation—namely, numerical analysis, theory of computability, and theory of finite automata. The chapter explores what practical results can be expected from a suitable mathematical theory. Further, the chapter presents several descriptive formalisms with a few examples of their use and theories that enable to prove the equivalence of computations expressed in these formalisms. A few mathematical results about the properties of the formalisms are also presented.

A Basis for a Mathematical Theory of Computation

In this paper, we examine an argument-based semantics called semi-stable semantics. Semi-stable semantics is quite close to traditional stable semantics in the sense that every stable extension is also a semi-stable extension. One of the advantages of semi-stable semantics is that there exists at least one semi-stable extension. Furthermore, if there also exists at least one stable extension, then the semi-stable extensions coincide with the stable extensions. This, and other properties, make semi-stable semantics an attractive alternative for the more traditional stable semantics, which until now has been widely used in fields such as logic programming and answer set programming.

/pdf/semi-stable-semantics-2q6ow9khu8.pdf

Semi-Stable Semantics

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ACM Transactions on Database Systems

We introduce a declarative approach for a coherent composition of autonomous databases. For this we use ID-logic, a formalism that extends classical logic with inductive definitions. We consider ID-logic theories that express, at the same time, the two basic challenges in database composition problems: relating different schemas of the local databases to one global schema (schema integration) and amalgamating the distributed and possibly contradictory data to one consistent database (data integration). We show that our framework supports different methods for schema integration (as well as their combinations) and that it provides a straightforward way of dealing with inconsistent data. Moreover, this framework facilitates the implementation of database repair and consistent query answering by means of a variety of reasoning systems.

/pdf/an-id-logic-formalization-of-the-composition-of-autonomous-4neumik56v.pdf

An ID-logic formalization of the composition of autonomous databases

Non-deterministic matrices, a natural generalization of many-valued matrices, are semantic structures in which the value assigned to a complex formula may be chosen non-deterministically from a given set of options. We show that by combining Nmatrices and preferential metric-based considerations, one obtains a family of logics that are useful for reasoning with uncertainty. We investigate the basic properties of these logics and demonstrate their usefulness in handling incomplete and inconsistent information.

/pdf/reasoning-with-uncertainty-by-nmatrix-metric-semantics-4iifhtp1s7.pdf

Reasoning with Uncertainty by Nmatrix---Metric Semantics

Distance-based reasoning is a well-known approach for defining non-monotonic and paraconsistent formalisms, which so far has been mainly used in the context of standard two-valued semantics. In this paper, we extend this approach to arbitrary denotational semantics by considering dissimilarities, a generalization of distances. Dissimilarity-based reasoning is then applied for handling inconsistency in knowledge-based systems using various non-classical logics. This includes logics defined by multi-valued semantics, non-deterministic semantics, and possible-worlds (Kripke-style) semantics. In particular, we show that our approach allows to define a variety of inconsistency-tolerant entailment relations, and that it extends many well-studied forms of reasoning in the context of belief revision and database integration.

Inconsistency-Tolerance in knowledge-based systems by dissimilarities

This paper extends the result of Caminada and Schulz [6, 7] by showing that assumption-based argumentation can represent not only normal logic programs, but also disjunctive logic programs. For this, we incorporate a previous work of ours (see [19, 20]), in which reasoning with assumption-based argumentation frameworks is based on certain core logics and the strict/defeasible assumptions may be arbitrary formulas in those logics. In our case, the core logic respects some inference rules for disjunction, which allows disjunctions in the heads of the programs’ rules to be handled properly.

An Argumentative Characterization of Disjunctive Logic Programming.

We introduce a preferential-based setting for reasoning with different types of argumentation-based semantics, including those that are not necessarily conflict-free or admissible. The induced entailments are defined by n-valued labeling and may be computed by answer-set programs.

http://comma2014.arg.dundee.ac.uk/res/pdfs/09-arieli.pdf

Ofer Arieli

Papers

An ID-logic formalization of the composition of autonomous databases

Reasoning with Uncertainty by Nmatrix---Metric Semantics

Inconsistency-Tolerance in knowledge-based systems by dissimilarities

An Argumentative Characterization of Disjunctive Logic Programming.

Preferential Reasoning Based On Abstract Argumentation Semantics.