Satisfiability Testing for Boolean Formulas Using Δ-trees

The tree-based data structure of -tree for propositional formulas is introduced in an improved and optimised form. The -trees allow a compact representation for negation normal forms as well as for a number of reduction strategies in order to consider only those occurrences of literals which are relevant for the satisfiability of the input formula. These reduction strategies are divided into two subsets (meaning- and satisfiability-preserving transformations) and can be used to decrease the size of a negation normal form A at (at most) quadratic cost. The reduction strategies are aimed at decreasing the number of required branchings and, therefore, these strategies allow to limit the size of the search space for the SAT problem.     

Ideology,inquiry, and antiquity: a critical notice of Lloyd's The Ideals of Inquiry: An Ancient History

A discussion of Lloyd's Tarner Lectures at Trinity College. The importance of Lloyd's previous scholarship is characterized and these sweeping, erudite lectures are placed in the context of that scholarship. In the broadest terms, the lectures are a call to culturally and historically comparative study of human reasoning. At their heart is a comparative history of scientific theorizing from the ancients through to modern science. Lloyd rejects the positivist picture, and the view of modern and ancient science as discontinuous; he urges scholars to undertake comparative work on the ancient sciences in different traditions. This critical notice evaluates Lloyd's view and raises several questions for further reflection.     

Demea’s Dilemmas

This paper considers how Descartes's and Hume's sceptical challenges were appropriated by Christian Wolff and Johann Nicolaus Tetens specifically in the context of projects related to Kant's in the transcendental deduction. Wolff introduces Descartes's dream hypothesis as an obstacle to his account of the truth of propositions, or logical truth, which he identifies with the 'possibility' of empirical concepts. Tetens explicitly takes Hume's account of our idea of causality to be a challenge to the `reality' of transcendent concepts in general, a challenge he addresses by locating the source of this concept in the understanding rather than in the imagination. After considering this background, I turn to Kant's deployment of apparently traditional sceptical concerns at the outset of the transcendental deduction and argue that he does not there intend to introduce a global sceptical challenge and, accordingly, that there are historical grounds for doubting that the transcendental deduction is intended as an anti-sceptical argument.     

Algorithmic Proof Methods and Cut Elimination for Implicational Logics Part I: Modal Implication

In this work we develop goal-directed deduction methods for the implicational fragment of several modal logics. We give sound and complete procedures for strict implication of K, T, K4, S4, K5, K45, KB, KTB, S5, G and for some intuitionistic variants. In order to achieve a uniform and concise presentation, we first develop our methods in the framework of Labelled Deductive Systems [Gabbay 96]. The proof systems we present are strongly analytical and satisfy a basic property of cut admissibility. We then show that for most of the systems under consideration the labelling mechanism can be avoided by choosing an appropriate way of structuring theories. One peculiar feature of our proof systems is the use of restart rules which allow to re-ask the original goal of a deduction. In case of K, K4, S4 and G, we can eliminate such a rule, without loosing completeness. In all the other cases, by dropping such a rule, we get an intuitionistic variant of each system. The present results are part of a larger project of a goal directed proof theory for non-classical logics; the purpose of this project is to show that most implicational logics stem from slight variations of a unique deduction method, and from different ways of structuring theories. Moreover, the proof systems we present follow the logic programming style of deduction and seem promising for proof search [Gabbay and Reyle 84, Miller et al. 91].     

A Draft for Unifying Controversies in Philosophy of Science

The basic (negative and positive) methodological maxims of three currents of philosophy of science (logical empiricism, falsificationism, and postpositivism) are formulated. Many of these maxims (stratagems) are controversial, e.g., the stance about the nonsense of metaphysics, and that of its indispensability. The restricted validity of these maxims allows for their unification. Within the framework of most of them there may be a relationship of (synchronic, or diachronic) subordination of the contradicting desiderata. In this vein ten stratagems are formulated. This revised version was published online in August 2006 with corrections to the Cover Date.     

社会认知中归纳推论－演绎推论的不对称性现象

在社会知觉中,人们会较多的根据个体的行为表现推论其所具有的人格特质（归纳推论）,较少根据人格特质来推论个体的行为表现（演绎推论）,Maass将这一现象命名为归纳推论－演绎推论的不对称性,并在西方文化下验证了这一现象。刻板印象在这一不对称性现象中起着调节作用,行为信息与刻板印象是否一致影响了归纳推论,对与刻板印象一致的信息更易做出归纳推论,而对演绎推论没有影响。在不同的文化背景下,归纳推论－演绎推论的不对称性表现存在差异,东方文化下的个体对两种推论过程没有表现出明显的倾向性。本文介绍了这一现象的表现,并总结了产生这一社会现象的内在原因及相关的研究进展。     

Kant’s deductions of morality and freedom

It is commonly held that Kant ventured to derive morality from freedom in Groundwork III. It is also believed that he reversed this strategy in the second Critique, attempting to derive freedom from morality instead. In this paper, I set out to challenge these familiar assumptions: Kant’s argument in Groundwork III rests on a moral conception of the intelligible world, one that plays a similar role as the ‘fact of reason’ in the second Critique. Accordingly, I argue, there is no reversal in the proof-structure of Kant’s two works.     

Proper Semantics for Substructural Logics,from a Stalker Theoretic Point of View

We study filters in residuated structures that are associated with congruence relations (which we call -filters), and develop a semantical theory for general substructural logics based on the notion of primeness for those filters. We first generalize Stone’s sheaf representation theorem to general substructural logics and then define the primeness of -filters as being “points” (or stalkers) of the space, the spectrum, on which the representing sheaf is defined. Prime FL-filters will turn out to coincide with truth sets under various well known semantics for certain substructural logics. We also investigate which structural rules are needed to interpret each connective in terms of prime -filters in the same way as in Kripke or Routley-Meyer semantics. We may consider that the set of the structural rules that each connective needs in this sense reflects the difficulty of giving the meaning of the connective. A surprising discovery is that connectives , ⅋ of linear logic are linearly ordered in terms of the difficulty in this sense. Presented by Wojciech Buszkowski     

Harmonising natural deduction

Prawitz proved a theorem, formalising ‘harmony’ in Natural Deduction systems, which showed that, corresponding to any deduction there is one to the same effect but in which no formula occurrence is both the consequence of an application of an introduction rule and major premise of an application of the related elimination rule. As Gentzen ordered the rules, certain rules in Classical Logic had to be excepted, but if we see the appropriate rules instead as rules for Contradiction, then we can extend the theorem to the classical case. Properly arranged there is a thoroughgoing ‘harmony’, in the classical rules. Indeed, as we shall see, they are, all together, far more ‘harmonious’ in the general sense than has been commonly observed. As this paper will show, the appearance of disharmony has only arisen because of the illogical way in which natural deduction rules for Classical Logic have been presented.