An Exactification of the Monoid of Primitive Recursive Functions

We study the monoid of primitive recursive functions and investigate a onestep construction of a kind of exact completion, which resembles that of the familiar category of modest sets, except that the partial equivalence relations which serve as objects are recursively enumerable. As usual, these constructions involve the splitting of symmetric idempotents.     

Causation in a New Old Key

I argue (1) that it is not philosophically significant whether causation is linguistically represented by a predicate or by a sentence connective; (2) that there is no philosophically significant distinction between event- and states-of-affairs-causation; (3) that there is indeed a philosophically significant distinction between agent- and event-causation, and that event-causation must be regarded as an analog of agent-causation. Developing this point, I argue that event-causation's being in the image of agent-causation requires, mainly, (a) that the cause is temporally prior to the effect, (b) that the cause necessitates (is sufficient with necessity) for the effect. Causal necessity is explained as a derivative of nomological necessity, and finally, via a definition of the causal sentence connective, the logic of event-causation is shown to be a part of temporal modal logic.     

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探讨后腹腔镜下肾孟、输尿管切开取石的技术要点和临床应用价值。回顾性分析34例后腹腔镜肾盂、输尿管切开取石术的临床质料。男22例,女12例,肾盂结石10例,输尿管结石24例。结果34例成功完成腹腔镜取石术,手术时间40min～90min,平均58min,术中出血10ml～30ml,术后1例漏尿3d,术后3d～5d拔除后腹...     

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     

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.     

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     

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.