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

BLOCKIN BLOCKINÒ BLOCKIN× ½¸ÔÔº ¿ßß¿º ¿

ACM Transactions on Database Systems

We introduce a general approach for representing and reasoning with argumentation-based systems. In our framework arguments are represented by Gentzen-style sequents, attacks (conflicts) between arguments are represented by sequent elimination rules, and deductions are made by dynamic proof systems. This framework accommodates different languages and logics in which arguments may be represented, supports a variety of attack relations, and tolerates dynamic changes in the argumentation setting by revising derivations of assertions in light of new information.

http://comma2014.arg.dundee.ac.uk/res/pdfs/10-arieli.pdf

Dynamic Derivations for Sequent-Based Logical Argumentation

http://www2.mta.ac.il/~oarieli/Papers/jal15.pdf

Conflict-free and conflict-tolerant semantics for constrained argumentation frameworks

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 non-deterministic matrices and distance-based considerations, one obtains a family of logics that are useful for reasoning with uncertainty. These logics are a conservative extension of those that are obtained by standard (i.e., deterministic) distance-based semantics, and so usual distance-based methods (in the context of, e.g., belief revision, information integration, and social choice theory) are easily simulated within our framework. We investigate the basic properties of the distance-preferential non-deterministic logics, consider their application for reasoning with incomplete and inconsistent information, and show the correspondence between some particular entailments in our framework and well-known problems like max-SAT.

Distance-based non-deterministic semantics for reasoning with uncertainty

Bilaitices, which have been shown to be very useful in logic programming, are used here for recovering consistent data from an inconsistent knowledge-base. Our method is coaseroative in the sense that it considers the contradictory data as useless, and regards all the remaining information unaffected. This kind of approach is nonmonotonic and paraconsistent in nature.

/pdf/a-bilattice-based-approach-to-recover-consistent-data-from-3wo6nk3qlp.pdf

Ofer Arieli

Papers

Dynamic Derivations for Sequent-Based Logical Argumentation

Conflict-free and conflict-tolerant semantics for constrained argumentation frameworks

Distance-based non-deterministic semantics for reasoning with uncertainty

A Bilattice-based Approach to Recover Consistent Data from Inconsistent Knowledge-Bases

Reasoning with Prioritized Information by Iterative Aggregation of Distance Functions