On Finite Models of the Lambek Calculus

We study a class of finite models for the Lambek Calculus with additive conjunction and with and without empty antecedents. The class of models enables us to prove the finite model property for each of the above systems, and for some axiomatic extensions of them. This work strengthens the results of [3] where only product-free fragments of these systems are considered. A characteristic feature of this approach is that we do not rely on cut elimination in opposition to e.g. [5], [9].     

Algebraic Kripke Sheaf Semantics for Non-Classical Predicate Logics

In so-called Kripke-type models, each sentence is assigned either to true or to false at each possible world. In this setting, every possible world has the two-valued Boolean algebra as the set of truth values. Instead, we take a collection of algebras each of which is attached to a world as the set of truth values at the world, and obtain an extended semantics based on the traditional Kripke-type semantics, which we call here the algebraic Kripke semantics. We introduce algebraic Kripke sheaf semantics for super-intuitionistic and modal predicate logics, and discuss some basic properties. We can state the Gödel-McKinsey-Tarski translation theorem within this semantics. Further, we show new results on super-intuitionistic predicate logics. We prove that there exists a continuum of super-intuitionistic predicate logics each of which has both of the disjunction and existence properties and moreover the same propositional fragment as the intuitionistic logic.     

On Extensions of Intermediate Logics by Strong Negation

In this paper we will study the properties of the least extension n() of a given intermediate logic by a strong negation. It is shown that the mapping from to n() is a homomorphism of complete lattices, preserving and reflecting finite model property, frame-completeness, interpolation and decidability. A general characterization of those constructive logics is given which are of the form n (). This summarizes results that can be found already in [13,14] and [4]. Furthermore, we determine the structure of the lattice of extensions of n(LC).     

模糊容忍性与发散性思维的关系：不同认识兴趣的作用

有理论认为,模糊容忍性有助于个体发散性思维的发展,但部分实证研究却呈现出不一致的结论。本文考察了不同认识兴趣在模糊容忍性与发散性思维关系之间的中介和调节作用。结果发现：（1）I型认识兴趣在模糊容忍性和独创性、灵活性、流畅性间起完全中介作用;（2）模糊容忍性与独创性、灵活性的关系受到D型认识兴趣的调节,模糊容忍性与流畅性的关系不受D型认识兴趣的调节。     

Memory and epistemic conservatism

Much of the plausibility of epistemic conservatism derives from its prospects of explaining our rationality in holding memory beliefs. In the first two parts of this paper, I argue for the inadequacy of the two standard approaches to the epistemology of memory beliefs, preservationism and evidentialism. In the third, I point out the advantages of the conservative approach and consider how well conservatism survives three of the strongest objections against it. Conservatism does survive, I claim, but only if qualified in certain ways. Appropriately qualified, conservatism is no longer the powerful anti-skeptical tool some have hoped for, but a doctrine closely connected with memory.