Giles’s Game and the Proof Theory of Łukasiewicz Logic

In the 1970s, Robin Giles introduced a game combining Lorenzen-style dialogue rules with a simple scheme for betting on the truth of atomic statements, and showed that the existence of winning strategies for the game corresponds to the validity of formulas in Łukasiewicz logic. In this paper, it is shown that ‘disjunctive strategies’ for Giles’s game, combining ordinary strategies for all instances of the game played on the same formula, may be interpreted as derivations in a corresponding proof system. In particular, such strategies mirror derivations in a hypersequent calculus developed in recent work on the proof theory of Łukasiewicz logic. Presented by Daniele Mundici     

Impressions formed in response to public self-evaluation maintenance strategies

Two studies examined the impressions formed in response to public self-evaluation maintenance strategies. According to Tesser’s (1988) self-evaluation maintenance (SEM) model, a person who has been outperformed by a close other perceives the field of performance as less relevant to preserve self-evaluation. Tesser and Paulhus (1983) showed that this same strategy is used for the purpose of impression management, or public self-evaluation maintenance. The present research examined the SEM model variables from the view of impression formation. In the first study, information regarding field relevance and psychological closeness was conveyed by the experimenter. In this context, field relevance had a significant impact on perception of competence. In the other study, in which the information was conveyed by the target person, relevance and closeness influenced the perception of manipulativeness and sociability. The results are discussed in terms of the importance of investigating the SEM processes from the impression formation perspective.     

Nelson's Negation on the Base of Weaker Versions of Intuitionistic Negation

Constructive logic with Nelson negation is an extension of the intuitionistic logic with a special type of negation expressing some features of constructive falsity and refutation by counterexample. In this paper we generalize this logic weakening maximally the underlying intuitionistic negation. The resulting system, called subminimal logic with Nelson negation, is studied by means of a kind of algebras called generalized N-lattices. We show that generalized N-lattices admit representation formalizing the intuitive idea of refutation by means of counterexamples giving in this way a counterexample semantics of the logic in question and some of its natural extensions. Among the extensions which are near to the intuitionistic logic are the minimal logic with Nelson negation which is an extension of the Johansson's minimal logic with Nelson negation and its in a sense dual version — the co-minimal logic with Nelson negation. Among the extensions near to the classical logic are the well known 3-valued logic of Lukasiewicz, two 12-valued logics and one 48-valued logic. Standard questions for all these logics — decidability, Kripke-style semantics, complete axiomatizability, conservativeness are studied. At the end of the paper extensions based on a new connective of self-dual conjunction and an analog of the Lukasiewicz middle value ½ have also been considered.     

The Class of Extensions of Nelson's Paraconsistent Logic

The article is devoted to the systematic study of the lattice εN4_⊥ consisting of logics extending N4_⊥. The logic N4_⊥ is obtained from paraconsistent Nelson logic N4 by adding the new constant ⊥ and axioms ⊥ → p, p → ∼ ⊥. We study interrelations between εN4_⊥ and the lattice of superintuitionistic logics. Distinguish in εN4_⊥ basic subclasses of explosive logics, normal logics, logics of general form and study how they are relate. The author acknowledges support by the Alexander von Humboldt-Stiftung and by Counsil for Grants under RF President, project NSh - 2112.2003.1.     

Algebraic Aspects of Cut Elimination

We will give here a purely algebraic proof of the cut elimination theorem for various sequent systems. Our basic idea is to introduce mathematical structures, called Gentzen structures, for a given sequent system without cut, and then to show the completeness of the sequent system without cut with respect to the class of algebras for the sequent system with cut, by using the quasi-completion of these Gentzen structures. It is shown that the quasi-completion is a generalization of the MacNeille completion. Moreover, the finite model property is obtained for many cases, by modifying our completeness proof. This is an algebraic presentation of the proof of the finite model property discussed by Lafont [12] and Okada-Terui [17].     

康德哲学与广松涉"交互主体的共同主观性"理论

广松涉认为,对近代认识论基础的问题式及其构成机制和局限进行反思,首先需要将着眼点放在康德哲学的问题式及其构成机制上。康德哲学的总的问题式就是在以先验逻辑学为基础的逻辑学、认识论和本体论“三位一体”的哲学构架中,探讨人的认识以及纯粹理性的先天综合判断及其能力何以可能。这一问题式潜含着一个意义非常重大的认识论问题——即“主体际共同主观性”问题．需要我们认真地加以研究。     

Conditionals and consequences

We examine the notion of conditionals and the role of conditionals in inductive logics and arguments. We identify three mistakes commonly made in the study of, or motivation for, non-classical logics. A nonmonotonic consequence relation based on evidential probability is formulated. With respect to this acceptance relation some rules of inference of System P are unsound, and we propose refinements that hold in our framework.