Protoalgebraic Gentzen Systems and the Cut Rule

In this paper we show that, in Gentzen systems, there is a close relation between two of the main characters in algebraic logic and proof theory respectively: protoalgebraicity and the cut rule. We give certain conditions under which a Gentzen system is protoalgebraic if and only if it possesses the cut rule. To obtain this equivalence, we limit our discussion to what we call regular sequent calculi, which are those comprising some of the structural rules and some logical rules, in a sense we make precise. We note that this restricted set of rules includes all the usual rules in the literature. We also stress the difference between the case of two-sided sequents and the case of many-sided sequents, in which more conditions are needed.     

Framing of imprecise quantities: When are lower interval bounds preferred to upper bounds?

Imprecisely known quantities (e.g., predictions) are often described in approximate terms as “more than X” or “less than Y” (e.g., “Ann will earn more than $50 000” or “less than $60 000”). Such phrases carry both quantitative and qualitative (pragmatic) information. Three studies are reported showing that lower limit estimates (more than, over, minimum) are generally more frequent, and considered more appropriate than upper limit estimates (less than, under, maximum) over a wide range of contexts. This is partly due to scalar properties of the number system, where lower numbers are attained before, and included in higher numbers, but not vice versa. As a result, upper limit statements are perceived as negations, and carry more specific information about the speaker's communicative concerns. Upper limit statements are preferred with amounts or quantities that can be perceived as small, whereas lower limit statements can be used both to indicate large quantities and as a default. Copyright © 2009 John Wiley & Sons, Ltd.     

强化降脂治疗的理性思考

他汀类药物因具有丰富的循征医学证据而成为一种不可缺少的预防和治疗冠状动脉粥样硬化性心脏病的降脂药物。近年来对高危患者提出强化降脂的概念,然而大剂量的他汀类药物的使用可能伴随着更多副作用及低效价比等问题。因此辨证地对待强化降脂的治疗策略是必要的。     

Type Logics and Pregroups

We discuss the logic of pregroups, introduced by Lambek [34], and its connections with other type logics and formal grammars. The paper contains some new ideas and results: the cut-elimination theorem and a normalization theorem for an extended system of this logic, its P-TIME decidability, its interpretation in L1, and a general construction of (preordered) bilinear algebras and pregroups whose universe is an arbitrary monoid. Special Issue Categorial Grammars and Pregroups Edited by Wojciech Buszkowski and Anne Preller     

Uniform Interpolation and Propositional Quantifiers in Modal Logics

We investigate uniform interpolants in propositional modal logics from the proof-theoretical point of view. Our approach is adopted from Pitts’ proof of uniform interpolationin intuitionistic propositional logic [15]. The method is based on a simulation of certain quantifiers ranging over propositional variables and uses a terminating sequent calculus for which structural rules are admissible. We shall present such a proof of the uniform interpolation theorem for normal modal logics K and T. It provides an explicit algorithm constructing the interpolants. Presented by Heinrich Wansing     

Sequent Calculi and Decision Procedures for Weak Modal Systems

We investigate sequent calculi for the weak modal (propositional) system reduced to the equivalence rule and extensions of it up to the full Kripke system containing monotonicity, conjunction and necessitation rules. The calculi have cut elimination and we concentrate on the inversion of rules to give in each case an effective procedure which for every sequent either furnishes a proof or a finite countermodel of it. Applications to the cardinality of countermodels, the inversion of rules and the derivability of Löb rules are given.     

On the Existence of Continua of Logics Between Some Intermediate Predicate Logics

A method for constructing continua of logics squeezed between some intermediate predicate logics, developed by Suzuki [8], is modified and applied to intervals of the form [L, L+ ¬¬S], where Lis a predicate logic, Sis a closed predicate formula. This solves one of the problems from Suzuki's paper.     

Supine defense in the intraspecific fighting of male house mice mus domesticus

House mice have been reported rarely to perform the supine behavior pattern as a defensive tactic during intraspecific fighting. However, in this study of intraspecific fighting by male mice, it is shown that mice do indeed rotate to supine. This maneuver is used to evade or extricate themselves from bites to the lower dorsum by the attacking opponent. Once free from the bite the defender does not remain supine, but will immediately turn to prone and flee. Remaining motionless in the supine position may serve a submissive function in other species, but this does not seem to be the case for mice. The present findings illustrate that the supine tactic is a dynamic maneuver for defense of body areas targeted by the opponent. © 1992 Wiley-Liss, Inc.