Algebraization, Parametrized Local Deduction Theorem and Interpolation for Substructural Logics over FL

Substructural logics have received a lot of attention in recent years from the communities of both logic and algebra. We discuss the algebraization of substructural logics over the full Lambek calculus and their connections to residuated lattices, and establish a weak form of the deduction theorem that is known as parametrized local deduction theorem. Finally, we study certain interpolation properties and explain how they imply the amalgamation property for certain varieties of residuated lattices. Dedicated to the memory of Willem Johannes Blok     

Minimal Varieties of Involutive Residuated Lattices

We establish the existence uncountably many atoms in the subvariety lattice of the variety of involutive residuated lattices. The proof utilizes a construction used in the proof of the corresponding result for residuated lattices and is based on the fact that every residuated lattice with greatest element can be associated in a canonical way with an involutive residuated lattice. Dedicated to the memory of Willem Johannes Blok     

The Beth Property in Algebraic Logic

The present paper is a study in abstract algebraic logic. We investigate the correspondence between the metalogical Beth property and the algebraic property of surjectivity of epimorphisms. It will be shown that this correspondence holds for the large class of equivalential logics. We apply our characterization theorem to relevance logics and many-valued logics. Dedicated to the memory of Willem Johannes Blok     

Interpolation and Definability in Guarded Fragments

The guarded fragment (GF) was introduced by Andréka, van Benthem and Németi as a fragment of first order logic which combines a great expressive power with nice, modal behavior. It consists of relational first order formulas whose quantifiers are relativized by atoms in a certain way. Slightly generalizing the admissible relativizations yields the packed fragment (PF). In this paper we investigate interpolation and definability in these fragments. We first show that the interpolation property of first order logic fails in restriction to GF and PF. However, each of these fragments turns out to have an alternative interpolation property that closely resembles the interpolation property usually studied in modal logic. These results are strong enough to entail the Beth definability property for GF and PF. Even better, every guarded or packed finite variable fragment has the Beth property. For interpolation, we characterize exactly which finite variable fragments of GF and PF enjoy this property.     

The ethical implications of the new research paradigm

Research is now an increasingly heterogeneous activity involving an expanded range of new actors and stake-holders and employing an eclectic range of epistemologies and methodologies. The emergence of these new research paradigms — and, in particular, of so-called ‘Mode 2’ knowledge production that is highly contextualised and socially distributed — raises new and challenging ethical issues and also important questions about the autonomy of science and the social responsibilities of scientists.     

Category coherence and category-based property induction

One important property of human object categories is that they define the sets of exemplars to which newly observed properties are generalized. We manipulated the causal knowledge associated with novel categories and assessed the resulting strength of property inductions. We found that the theoretical coherence afforded to a category by inter-feature causal relationships strengthened inductive projections. However, this effect depended on the degree to which the exemplar with the to-be-projected predicate manifested or satisfied its category's causal laws. That is, the coherence that supports inductive generalizations is a property of individual category members rather than categories. Moreover, we found that an exemplar's coherence was mediated by its degree of category membership. These results were obtained across a variety of causal network topologies and kinds of categories, including biological kinds, non-living natural kinds, and artifacts.     

The Distance Function in Commutative ℓ-semigroups and the Equivalence in Łukasiewicz Logic

The equivalence connective in ukasiewicz logic has its algebraic counterpart which is the distance function d(x,y) =|x–y| of a positive cone of a commutative -group. We make some observations on logically motivated algebraic structures involving the distance function.     

A Generalization of the Łukasiewicz Algebras

We introduce the variety _n ^m , m 1 and n 2, of m-generalized ukasiewicz algebras of order n and characterize its subdirectly irreducible algebras. The variety _n ^m is semisimple, locally finite and has equationally definable principal congruences. Furthermore, the variety _n ^m contains the variety of ukasiewicz algebras of order n.     

关系属性:动允性概念的方法论蕴含

动允性是指环境提供给有机体的行动可能性。1977年,生态心理学家吉布森首次提出了“动允性”概念。这一概念有着深刻的方法论含义。首先,动允性超越了传统二元论思维的束缚。它既不是环境方面的物理属性,也不是动物方面的主观属性,而是环境与动物交互作用中的一个关系属性。其次,动允性所体现出来的价值和意义与动允性的关系属性是一致的。它主张意义既不外显于事物的外部,也不隐藏于事物的内部,而是嵌入于有机体和环境的互动互补关系之中。最后,这种关系属性使它免于被归结为物理的或心理的性质,从而超越了还原论的思维方式。