Recent years have been blessed with an abundance of logical systems, arising from a multitude of applications. A logic can be characterised in many different ways. Traditionally, a logic is presented via the following three components: 1. an intuitive non-formal motivation, perhaps tie it in to some application area 2. a semantical interpretation 3. a proof theoretical formulation. There are several types of proof theoretical methodologies, Hilbert style, Gentzen style, goal directed style, labelled deductive system style, and so on. The (...) tableau methodology, invented in the 1950s by Beth and Hintikka and later per fected by Smullyan and Fitting, is today one of the most popular, since it appears to bring together the proof-theoretical and the semantical approaches to the pre of a logical system and is also very intuitive. In many universities it is sentation the style first taught to students. Recently interest in tableaux has become more widespread and a community crystallised around the subject. An annual tableaux conference is being held and proceedings are published. The present volume is a Handbook a/Tableaux pre senting to the community a wide coverage of tableaux systems for a variety of logics. It is written by active members of the community and brings the reader up to frontline research. It will be of interest to any formal logician from any area. (shrink)

Deductive inference is usually regarded as being “tautological” or “analytical”: the information conveyed by the conclusion is contained in the information conveyed by the premises. This idea, however, clashes with the undecidability of first-order logic and with the (likely) intractability of Boolean logic. In this article, we address the problem both from the semantic and the proof-theoretical point of view. We propose a hierarchy of propositional logics that are all tractable (i.e. decidable in polynomial time), although by means of growing (...) computational resources, and converge towards classical propositional logic. The underlying claim is that this hierarchy can be used to represent increasing levels of “depth” or “informativeness” of Boolean reasoning. Special attention is paid to the most basic logic in this hierarchy, the pure “intelim logic”, which satisfies all the requirements of a natural deduction system (allowing both introduction and elimination rules for each logical operator) while admitting of a feasible (quadratic) decision procedure. We argue that this logic is “analytic” in a particularly strict sense, in that it rules out any use of “virtual information”, which is chiefly responsible for the combinatorial explosion of standard classical systems. As a result, analyticity and tractability are reconciled and growing degrees of computational complexity are associated with the depth at which the use of virtual information is allowed. (shrink)

In our information societies, tasks and decisions are increasingly outsourced to automated systems, machines, and artificial agents that mediate human relationships, by taking decisions and acting on the basis of algorithms. This raises a critical issue: how are algorithmic procedures and applications to be appraised and governed? This question needs to be investigated, if one wishes to avoid the traps of ICTs ending up in isolating humans behind their screens and digital delegates, or harnessing them in a passive role, by (...) curtailing their freedom and autonomy. (shrink)

Free Public Reason examines the idea of public justification, stressing its importance but also questioning the coherence of the concept itself. Although public justification is employed in the work of theorists such as John Rawls, Jeremy Waldron, Thomas Nagel, and others, it has received little attention on its own as a philosophical concept. In this book Fred D'Agostino shows that the concept is composed of various values, interests, and notions of the good, and that no ranking of these is (...) possible. The notion of public justification itself is thus shown to be contestable. In demonstrating this, D'Agostino undermines many current political theories that rely on this concept. Having broken down the foundations of public justification, D'Agostino then offers an alternative model of how a workable consensus on its meaning might be reached through the interactions of a community of interpreters or delegates at a constitutional convention. (shrink)

We show that Smullyan's analytic tableaux cannot p-simulate the truth-tables. We identify the cause of this computational breakdown and relate it to an underlying semantic difficulty which is common to the whole tradition originating in Gentzen's sequent calculus, namely the dissonance between cut-free proofs and the Principle of Bivalence. Finally we discuss some ways in which this principle can be built into a tableau-like method without affecting its analytic nature.

This book was published in 2003.This volume presents a detailed examination of incommensurability in the value-theoretical sense. Exploring how choosers deal with problems and constraints of choice, the author draws on work in cognitive psychology, in sociology, in jurisprudence, in economics, and in the theory of value to show how choosers learn to make trade-offs when there is potential incommensurability among the options they are considering. The analysis is also informed by recent work in the tradition of Michel Foucault. With (...) so many modern devices and ideals of government dependent on the comparability of options, this book is timely and can inform public debate about de-regulation, user-pays, accountability, and the substitution of market mechanisms for government regulation and supply. (shrink)

We have considered two strategies for using native utterances as evidence for assigning native beliefs. We have shown that each of these two strategies (literalism and symbolism) can avoid the logical difficulties mentioned in section 1 — so long, at least, as we employ an account of the logical form of belief sentences developed by Burdick. We have also considered the methodological principles which provide the basis for translational practice. Based on our consideration of these principles, we then argued that (...) we must prefer the literalist strategy for attributing beliefs. Only the literalist strategy enables us to provide a recursive account of the significance of native utterances, and only the literalist strategy enables us to maximize the truth of our claims about native beliefs. (shrink)

This book examines the most controversial issues concerning the use of pre-drafted clauses in fine print, which are usually included in consumer contracts and presented to consumers on a take-it-or-leave-it basis. By applying a multi-disciplinary approach that combines consumer's psychology and seller's drafting power in the logic of efficiency and good faith, the book provides a fresh and unconventional analysis of the existing literature, both theoretical and empirical. Moving from the unconscionability doctrine, it criticizes (and in some cases refutes) its (...) main conclusions based on criteria which are usually invoked to sustain the need for public intervention to protect consumers, and specifically related to Law (contract complexity), Psychology (consumer lack of sophistication criterion) and Economics (market structure criterion). It also analyzes the effects of different regulations, such as banning vexatious clauses or mandating disclosure clauses, showing that none of them protect consumers, but in fact prove to be harmful when consumers are more vulnerable, that is whenever sellers can exploit some degree of market power. In closing, the book combines these disparate aspects, arguing that the solution (if any) to the problem of consumer exploitation and market inefficiency associated with the use of contracts of adhesion in these contexts cannot be found in removing or prohibiting hidden clauses, but instead has to take into account the effects of these clauses on the contract as a whole. (shrink)

Institutions associated with the idea of opposition play a crucial role in democracy: “[i]f it is to work, it requires an extraordinarily sophisticated human attitude—that of loyal [and tolerated] opposition.”.

In his renowned collection Philosophy as a Way of Life, Pierre Hadot suggests that the original trait of philosophy as a method by which one exercises themselves to achieve a new way of living and seeing the world fails with the rise of modernity. In that time, philosophy increasingly takes on a merely theoretical aspect, tending toward a system. However, Hadot himself glimpses at the dawn of modernity some instances of the original trait of philosophy still very much present, and (...) in his wake, Michel Foucault warns that between the late 16th and early 17th centuries the philosophical question of the reform of the mind attests to a still very close link between asceticism and truth. This book aims to develop just such an idea by thoroughly analyzing the most representative works of the reform of the mind in the early modern period: Francis Bacon's New Organon (1620), René Descartes' Discourse on the Method (1637), and Baruch Spinoza's Treatise on the Emendation of the Intellect (1677). From this analysis it will emerge that these modern works fully deserve to be counted among the tradition of philosophy as way of life. On closer inspection, the inquiries about method elaborated in these works are fully understandable only when read in the light of a broader and more complex philosophical need: to establish the spiritual conditions for accessing truth and aspiring to full self-realization. (shrink)

Today some scholars consider Descartes a virtue epistemologist. In my paper, I examine this position, making a positive contribution to his claim. After a brief clarifying premise about the meaning and scope of virtue epistemology, I present two major theoretical positions that argue, in a different way, that Descartes can be considered a virtue epistemologist: that of Ernest Sosa, usually acknowledged as virtue reliabilism; that of Richard Davies, more inclined towards a so called responsibilist virtue epistemology. Finally, I deal myself (...) directly with some specific Cartesian texts, especially from the Discours de la méthode, in order to draw elements for strengthen and deepen the previous positions, thanks mostly to the passion virtue of generosity. (shrink)

We investigate the semantics of the logical systems obtained by introducing the modalities and into the family of substructural implication logics (including relevant, linear and intuitionistic implication). Then, in the spirit of the LDS (Labelled Deductive Systems) methodology, we "import" this semantics into the classical proof system KE. This leads to the formulation of a uniform labelled refutation system for the new logics which is a natural extension of a system for substructural implication developed by the first two authors in (...) a previous paper. (shrink)

We consider the relation between the uniform interpolation property and the elimination of non-standard quantifiers (the bisimulation quantifiers) in the context of the ?-calculus. In particular, we isolate classes of frames where the correspondence between these two properties is nicely smooth.

Book Information Relativism. By Paul O'Grady. Acumen. Chesham. 2002. Pp. xi + 196. Paperback, £12.95.