Voting by Eliminating Quantifiers

Mathematical theory of voting and social choice has attracted much attention. In the general setting one can view social choice as a method of aggregating individual, often conflicting preferences and making a choice that is the best compromise. How preferences are expressed and what is the “best compromise” varies and heavily depends on a particular situation. The method we propose in this paper depends on expressing individual preferences of voters and specifying properties of the resulting ranking by means of first-order formulas. Then, as a technical tool, we use methods of second-order quantifier elimination to analyze and compute results of voting. We show how to specify voting, how to compute resulting rankings and how to verify voting protocols.     

Independence — Revision and Defaults

We investigate different aspects of independence here, in the context of theory revision, generalizing slightly work by Chopra, Parikh, and Rodrigues, and in the context of preferential reasoning.     

Semantics for Higher Level Attacks in Extended Argumentation Frames Part 1: Overview

In 2005 the author introduced networks which allow attacks on attacks of any level. So if a → b reads a attacks b, then this attack can itself be attacked by another node c. This attack itself can attack another node d. This situation can be iterated to any level with attacks and nodes attacking other attacks and other nodes. In this paper we provide semantics (of extensions) to such networks. We offer three different approaches to obtaining semantics.

1. The translation approach This uses the methodology of ‘Logic by translation’. We translate faithfully the new networks into ordinary Dung networks with more nodes and extract the semantics from the translation.
2. The labelling approach This method regards the arrows as additional entities to be attacked and to mount attacks and applies a variation of the usual machinery of Camindada like labelling to the network. The new concept we need to employ here is that of ‘joint attacks’.
3. The logic programming approach We translate the higher level network into a logic program and obtain semantics for it through known semantics for logic programs.

We then compare our methods with those of S. Modgil and P. M. Dung et al.     

A Logical Account of Formal Argumentation

In the current paper, we re-examine how abstract argumentation can be formulated in terms of labellings, and how the resulting theory can be applied in the field of modal logic. In particular, we are able to express the (complete) extensions of an argumentation framework as models of a set of modal logic formulas that represents the argumentation framework. Using this approach, it becomes possible to define the grounded extension in terms of modal logic entailment.     

On Modal Logics Characterized by Models with Relative Accessibility Relations: Part II

This work is divided in two papers (Part I and Part II). In Part I, we introduced the class of Rare-logics for which the set of terms indexing the modal operators are hierarchized in two levels: the set of Boolean terms and the set of terms built upon the set of Boolean terms. By investigating different algebraic properties satisfied by the models of the Rare-logics, reductions for decidability were established by faithfully translating the Rare-logics into more standard modal logics (some of them contain the universal modal operator).In Part II, we push forward the results from Part I. For Rare-logics with nominals (present at the level of formulae and at the level of modal expressions), we show that the constructions from Part I can be extended although it is technically more involved. We also characterize a class of standard modal logics for which the universal modal operator can be eliminated as far as satifiability is concerned. Although the previous results have a semantic flavour, we are also able to define proof systems for Rare-logics from existing proof systems for the corresponding standard modal logics. Last, but not least, decidability results for Rare-logics are established uniformly, in particular for information logics derived from rough set theory.Since this paper is the continuation of Part I, we do not recall here the definitions of Part I although we refer to them.     

Preattentive processing or prefocal processing?

The concept of preattentive processing is analyzed and alternative views of it are presented. A basic question is whether processing required for preattentive input selection is qualitatively different from post-selection processing. In order to study this, subjects were presented in one set of conditions with one stimulus at either of two locations, and in another set of conditions, simultaneously with two stimuli. The stimuli could be green or red, or large or small. Subjects were asked to indicate the location (or the color, or the size) of the single stimulus in the single-stimulus conditions, or of a predesignated stimulus (say, the red one) in the dual-stimulus conditions. Responses were generally slower in the dual-stimulus conditions. The increases in reaction time were accounted for by the times it takes to process for response selection the properties by which the target stimulus could be selected, as indicated by the results of two control conditions. The results as well as some other considerations do not support the view that preattentive processing is necessarily of a type that qualitatively differs from post-selection processing.     

THE ILLIBERALITY OF ‘LIBERAL EUGENICS’

This essay evaluates the moral logic of ‘liberal eugenics’: the ideal of genetic control which leaves decisions about what sort of people to produce in the hands of individual parents, absent government intervention. I argue that liberal eugenics cannot be justified on the basis of the underlying liberal theory which inspires it. I introduce an alternative to Rawls's social primary goods that might be called natural primary goods: hereditable mental and physical capacities and dispositions that are valued across a range of projects and pursuits. I suggest that reproductive genetic biotechnologies like embryo selection, cellular surgery, and genetic engineering, which aim to enhance ‘general purpose’ traits in offspring are less like childrearing practices a liberal government leaves to the discretion of parents than like practices the state makes compulsory. I argue that if the liberal commitment to autonomy is important enough for the state to mandate childrearing practices such as health care and basic education, that very same interest is important enough for the state to mandate safe, effective, and functionally integrated genetic practices that act on analogous all‐purpose traits such as resistance to disease and general cognitive functioning. I conclude that the liberal case for compulsory eugenics is a reductio against liberal theory.