Adaptive logics using the minimal abnormality strategy are $$\Pi^1_1$$ -complex

In this article complexity results for adaptive logics using the minimal abnormality strategy are presented. It is proven here that the consequence set of some recursive premise sets is -complete. So, the complexity results in (Horsten and Welch, Synthese 158:41–60, 2007) are mistaken for adaptive logics using the minimal abnormality strategy.     

SUPERVALUATION FIXED-POINT LOGICS OF TRUTH

Michael Kremer defines fixed-point logics of truth based on Saul Kripke’s fixed point semantics for languages expressing their own truth concepts. Kremer axiomatizes the strong Kleene fixed-point logic of truth and the weak Kleene fixed-point logic of truth, but leaves the axiomatizability question open for the supervaluation fixed-point logic of truth and its variants. We show that the principal supervaluation fixed point logic of truth, when thought of as consequence relation, is highly complex: it is not even analytic. We also consider variants, engendered by a stronger notion of ‘fixed point’, and by variant supervaluation schemes. A ‘logic’ is often thought of, not as a consequence relation, but as a set of sentences – the sentences true on each interpretation. We axiomatize the supervaluation fixed-point logics so conceived.     

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     

Line-based affine reasoning in Euclidean plane

We consider the binary relations of parallelism and convergence between lines in a 2-dimensional affine space. Associating with parallelism and convergence the binary predicates P and C and the modal connectives [P] and [C], we consider a first-order theory based on these predicates and a modal logic based on these modal connectives. We investigate the axiomatization/completeness and the decidability/complexity of this first-order theory and this modal logic.     

论“后天八卦”中的数理内涵──兼论《禹贡》和《太玄》对称三进制

"先天八卦"中具有数理内涵,同样,"后天八卦"中亦具有数理内涵。前者呈二进制形态,后者则为三进制形态。《系辞》曰:"太极生两仪,两仪生四象,四象生八卦。"其实,四象生八卦有两种不同的逻辑法则,这两种不同的逻辑法则导致二进制八卦与三进制八卦。而且"后天八卦"与五行具有内在的关联,因此,"后天八卦"中的数理内涵比"先天八卦"中的数理内涵更显丰富。     

Glivenko Type Theorems for Intuitionistic Modal Logics

In this article we deal with Glivenko type theorems for intuitionistic modal logics over Prior's MIPC. We examine the problems which appear in proving Glivenko type theorems when passing from the intuitionistic propositional logic Intto MIPC. As a result we obtain two different versions of Glivenko's theorem for logics over MIPC. Since MIPCcan be thought of as a one-variable fragment of the intuitionistic predicate logic Q-Int, one of the versions of Glivenko's theorem for logics over MIPCis closely related to that for intermediate predicate logics obtained by Umezawa [27] and Gabbay [15]. Another one is rather surprising.     

Free-Variable Tableaux for Propositional Modal Logics

Free-variable semantic tableaux are a well-established technique for first-order theorem proving where free variables act as a meta-linguistic device for tracking the eigenvariables used during proof search. We present the theoretical foundations to extend this technique to propositional modal logics, including non-trivial rigorous proofs of soundness and completeness, and also present various techniques that improve the efficiency of the basic naive method for such tableaux.     

Three Complexity Problems in Quantified Fuzzy Logic

We prove that the sets of standard tautologies of predicate Product Logic and of predicate Basic Logic, as well as the set of standard-satisfiable formulas of predicate Basic Logic are not arithmetical, thus finding a rather satisfactory solution to three problems proposed by Hájek in [H01].     

空间-时间关联的中介共同表征结构:来自反转STEARC效应的证据

通过3个双任务实验(诱导任务和特征任务)探讨空间-时间联合编码(STEARC)效应的加工机制。实验1采用时间信息作为诱导任务材料,实验2采用空间信息作为诱导任务材料,在特征任务中都发现映射不一致组被试(看到过去/左侧刺激时按右键反应,看到未来/右侧刺激时按左键反应)出现反转STEARC效应,映射一致组被试表现出常规的STEARC效应,表明从时间信息加工到空间反应过程符合中介共同表征结构。实验3分离两种任务的反应方式(手动和眼动),发现不一致映射规则下,被试仍然表现出常规的STEARC效应,表明这种中介共同表征结构存在特定联结效应,即在不同反应器中出现时间和空间相互独立的表征结构。总体而言,研究支持空间-时间关联符合中介共同表征结构,并且这种关联中存在反应器特定联结效应。