A Short Note on Gentzen's LJ and NJ Systems Isomorphism

By Wagner Sanz

We state a new intuitionistic sequent calculus and use it to clarify Gentzen's NJ and LJ isomorphism, it contains new negation rules which are immediate readings of what seems to be good and sound natural deduction rules.
Keywords: Sequent Calculus, Natural Deduction, Intuitionism, Negation.

Source: CLE e-prints

Posted by Tony Marmo at 16:58 BST

Updated: Tuesday, 16 May 2006 17:02 BST

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A game-theoretic account of implicature

By Prashant Parikh

I use game theory, decision theory, and situation theory to model a class of implicatures. Two types of relevance are distinguished and used to construct a model of Gricean communication between speaker and addressee.

Source: Proceedings of the 4th conference on Theoretical aspects of reasoning about knowledge, Monterey, California, Pages: 85 - 94 Year of Publication: 1992

Posted by Tony Marmo at 16:46 BST

Updated: Friday, 5 May 2006 16:50 BST

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A Logic for Ambiguous Description

By Arthur Buchsbaum

A logic formalizing ambiguity, which appears both in natural language and in mathematical discourse, is presented, through a sequent calculus and a semantics, together with some elementary results.

Author Keywords: ambiguous description; designators; rigidity
Appeared in 'Electronic Notes in Theoretical Computer Science' Volume 67, October 2002, Pages 1-18 WoLLIC'2002, 9th Workhop on Logic, Language, Information and Computation

Posted by Tony Marmo at 14:44 BST

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Conditional Excluded Middle in Systems of Consequential Implication

By Claudio Pizzi & Timothy Williamson

It is natural to ask under what conditions negating a conditional is equivalent to negating its consequent. Given a bivalent background logic, this is equivalent to asking about the conjunction of Conditional Excluded Middle (CEM, opposite conditionals are not both false) and Weak Boethius’ Thesis (WBT, opposite conditionals are not both true). In the system CI.0 of consequential implication, which is intertranslatable with the modal logic KT, WBT is a theorem, so it is natural to ask which instances of CEM are derivable. We also investigate the systems CIw and CI of consequential implication, corresponding to the modal logics K and KD respectively, with occasional remarks about stronger systems. While unrestricted CEM produces modal collapse in all these systems, CEM restricted to contingent formulas yields the Alt2 axiom (semantically, each world can see at most two worlds), which corresponds to the symmetry of consequential implication. It is proved that in all the main systems considered, a given instance of CEM is derivable if and only if the result of replacing consequential implication by the material biconditional in one or other of its disjuncts is provable. Several related results are also proved. The methods of the paper are those of propositional modal logic as applied to a special sort of conditional.

Appeared at the Journal of Philosophical Logic 34, 4 (2005): 333-362

Posted by Tony Marmo at 05:58 BST

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Gestalt Effects in Counterfactual and Abductive Inference

By Claudio Pizzi

This paper begins by focusing the basic idea that Gestalt phenomena belong not only to the realm of perception but to the realm of inference. It is shown that Gestalt effects (i.e. the derivability of incompatible indifferent conclusions on the basis of the same background information) often occur both in counterfactual and in ampliative – i.e. inductive and abductive – reasoning. The main thesis of the paper is that the common feature of such forms of non-deductive reasoning is provided by a rational selection between incompatible conclusions, where rationality lies in the choice of the alternative which preserves the maximum of background information. It is also stressed a distinction between a weak and a strong notion of incompatibility. Such distinction may help in giving account of some alleged Gestalt phenomena which have been recognized in theory construction and theory change.

Keywords: Abduction, Counterfactuals, Induction, Gestalt, Rationality

To appear in the L. J. of the IGPL

Posted by Tony Marmo at 00:01 BST

Updated: Wednesday, 12 April 2006 05:49 BST

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Flexible Temporal Consistency for Fixed-Time Constraint Verification in Grid Workflow Systems

By Jinjun Chen & Yun Yang

To verify fixed-time constraints in grid workflow systems, the consistency and inconsistency conditions have been defined in the conventional work. However, in this paper, we argue that although the conventional consistency condition is reasonable, the conventional inconsistency condition is too rigorous and covers several different situations. These situations which are handled conventionally by the same exception handling should be handled differently for cost saving. Therefore, we divide the conventional inconsistency into weak consistency,weak inconsistency and strong inconsistency and treat the conventional consistency as strong consistency. Correspondingly, we discuss how to verify them. Especially, for the weak consistency, we present a method on how to adjust it to the strong consistency. For the weak inconsistency, we analyse why it can be handled by simpler and more economical exception handling. The final comparison and discussion further demonstrate that our research can achieve better cost effectiveness than the conventional work.

Appeared in Lecture Notes in Computer Science, Volume 3795 / 2005

Posted by Tony Marmo at 01:16 BST

Updated: Saturday, 8 April 2006 01:18 BST

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Counterfactuals in a Dynamic Context

By Kai von Fintel

This paper has presented a sketch of an alternative implementation of the standard possible worlds semantics of counterfactuals.

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The Presupposition of Subjunctive Conditionals

By Kai von Fintel

Why are some conditionals subjunctive? It is often assumed that at least one crucial difference is that subjunctive conditionals presuppose that their antecedent is false, that they are counterfactual (Lakoff 1970). The traditional theory has apparently been refuted. Perhaps the clearest counter-example is one given by Alan Anderson (1951: 37): If Jones had taken arsenic, he would have shown just exactly those symptoms which he does in fact show. A typical place to use such a subjunctive conditional would be in the course of an argument that tries to bolster the hypothesis that Jones did in fact take arsenic. But then it would of course be self-defeating to presuppose that the hypothesis is false. Thus, something else must be going on.

Posted by Tony Marmo at 00:01 BST

Updated: Friday, 7 April 2006 01:45 BST

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