On Conservative Extensions in Logics with Infinitary Predicates

If the language is extended by new individual variables, in classical first order logic, then the deduction system obtained is a conservative extension of the original one. This fails to be true for the logics with infinitary predicates. But it is shown that restricting the commutativity of quantifiers and the equality axioms in the extended system and supposing the merry-go-round property in the original system, the foregoing extension is already conservative. It is shown that these restrictions are crucial for an extension to be conservative. The origin of the results is algebraic logic. Presented by Daniele Mundici Supported by grant OTKA T43242.     

Reasoning about cooperation,actions and preferences

In this paper, a logic for reasoning about coalitional power is developed which explicitly represents agents’ preferences and the actions by which the agents can achieve certain results. A complete axiomatization is given and its satisfiability problem is shown to be decidable and EXPTIME-hard.     

基于非逻辑机制的条件推理模式：P—Q映射模型及其实证检验

研究结合数学分析方法,提出了基于非逻辑机制的条件推理模型：P-Q映射模型。并根据这个模型,对人们在不同命题类型奈件下的推理行为进行了预测。预测结果显示,当推理前提为LH和HL型命题时,基于P-Q映射模型的预测结果与基于条件概率模型的预测结果完全一致。但当推理前提为LL和HH型命题时,两种模型给出的预测结果存在差异。实验结果表明,当前提命题为LL和HH型命题时,被试的条件推理行为与P-Q映射模型的预言完全一致。     

Categorical Abstract Algebraic Logic: Prealgebraicity and Protoalgebraicity

Two classes of π are studied whose properties are similar to those of the protoalgebraic deductive systems of Blok and Pigozzi. The first is the class of N-protoalgebraic π-institutions and the second is the wider class of N-prealgebraic π-institutions. Several characterizations are provided. For instance, N-prealgebraic π-institutions are exactly those π-institutions that satisfy monotonicity of the N-Leibniz operator on theory systems and N-protoalgebraic π-institutions those that satisfy monotonicity of the N-Leibniz operator on theory families. Analogs of the correspondence property of Blok and Pigozzi for π-institutions are also introduced and their connections with preand protoalgebraicity are explored. Finally, relations of these two classes with the (, N)-algebraic systems, introduced previously by the author as an analog of the -algebras of Font and Jansana, and with an analog of the Suszko operator of Czelakowski for π-institutions are also investigated. Presented by Josep Maria Font     

Combinatory Logic and the Semantics of Substructural Logics

The results of this paper extend some of the intimate relations that are known to obtain between combinatory logic and certain substructural logics to establish a general characterization theorem that applies to a very broad family of such logics. In particular, I demonstrate that, for every combinator X, if LX is the logic that results by adding the set of types assigned to X (in an appropriate type assignment system, TAS) as axioms to the basic positive relevant logic B∘T, then LX is sound and complete with respect to the class of frames in the Routley-Meyer relational semantics for relevant and substructural logics that meet a first-order condition that corresponds in a very direct way to the structure of the combinator X itself. Presented by Rob Goldblatt     

A Deep Inference System for the Modal Logic S5

We present a cut-admissible system for the modal logic S5 in a formalism that makes explicit and intensive use of deep inference. Deep inference is induced by the methods applied so far in conceptually pure systems for this logic. The system enjoys systematicity and modularity, two important properties that should be satisfied by modal systems. Furthermore, it enjoys a simple and direct design: the rules are few and the modal rules are in exact correspondence to the modal axioms. Presented by Heinrich Wansing     

Parsing Pregroup Grammars and Lambek Calculus Using Partial Composition

The paper presents a way to transform pregroup grammars into contextfree grammars using functional composition. The same technique can also be used for the proof-nets of multiplicative cyclic linear logic and for Lambek calculus allowing empty premises.     

逻辑训练对不同理性思维方式大学生三段论推理的影响

采用理性—经验思维方式量表对105名大学生进行测量,选出高、低理性思维方式各35名大学生进行实验,探讨了逻辑训练对不同理性思维方式大学生三段论推理的影响。结果表明：(1)高理性思维方式个体三段论推理的平均反应时快于低理性思维方式个体;非冲突类型题目推理的平均正确率高于冲突类型题目;逻辑训练可以提高个体三段论推理的平均反应时和正确率;(2)逻辑训练后非冲突任务类型题目的平均正确率高于冲突任务类型题目;(3)逻辑训练对低理性思维方式个体冲突任务类型题目平均正确率的提高效果更明显。这意味着逻辑训练可以显著提升个体的推理成绩,但不能完全消除信念偏差对推理的影响,而且逻辑训练对低理性思维方式个体推理成绩的提升效果更加明显。