Types of \mathsf{I} -Free Hereditary Right Maximal Terms

The implicational fragment of the relevance logic “ticket entailment” is closely related to the so-called hereditary right maximal terms. I prove that the terms that need to be considered as inhabitants of the types which are theorems of T_→ are in normal form and built in all but one case from and only. As a tool in the proof ordered term rewriting systems are introduced. Based on the main theorem I define FIT_→ – a Fitch-style calculus (related to FT_→) for the implicational fragment of ticket entailment.     

On Dynamic Topological and Metric Logics

We investigate computational properties of propositional logics for dynamical systems. First, we consider logics for dynamic topological systems (W.f), fi, where W is a topological space and f a homeomorphism on W. The logics come with ‘modal’ operators interpreted by the topological closure and interior, and temporal operators interpreted along the orbits {w, f(w), f² (w), ˙˙˙} of points w ε W. We show that for various classes of topological spaces the resulting logics are not recursively enumerable (and so not recursively axiomatisable). This gives a ‘negative’ solution to a conjecture of Kremer and Mints. Second, we consider logics for dynamical systems (W, f), where W is a metric space and f and isometric function. The operators for topological interior/closure are replaced by distance operators of the form ‘everywhere/somewhere in the ball of radius a, ‘for a ε Q ⁺. In contrast to the topological case, the resulting logic turns out to be decidable, but not in time bounded by any elementary function.     

抽象材料选择任务的表象表征视角

为了探讨在选择任务中表象表征存在的可能性以及抽象材料选择任务困难的原因,该研究设定了材料的内容、规则以及证明规则的要求均完全相同,只是在呈现方式上形象性不同的两种抽象选择任务;然后把两种不同的选择任务分别对数量大致相当的大学生进行了测试。结果发现,不采用类似卡片这种形象性很强的材料呈现方式显著的提高了人们在抽象选择任务中的正确率。实验结果支持了选择任务中表象表征的存在及其为选择任务困难原因之一的观点。     

Decidable Cases of First-order Temporal Logic with Functions

We consider the decision problem for cases of first-order temporal logic with function symbols and without equality. The monadic monodic fragment with flexible functions can be decided with EXPSPACE-complete complexity. A single rigid function is sufficient to make the logic not recursively enumerable. However, the monadic monodic fragment with rigid functions, where no two distinct terms have variables bound by the same quantifier, is decidable and EXPSPACE-complete. Presented by Robert Goldblatt     

Constructive Logic with Strong Negation is a Substructural Logic. II

The goal of this two-part series of papers is to show that constructive logic with strong negation N is definitionally equivalent to a certain axiomatic extension NFL _ew of the substructural logic FL _ew . The main result of Part I of this series [41] shows that the equivalent variety semantics of N (namely, the variety of Nelson algebras) and the equivalent variety semantics of NFL _ew (namely, a certain variety of FL _ew -algebras) are term equivalent. In this paper, the term equivalence result of Part I [41] is lifted to the setting of deductive systems to establish the definitional equivalence of the logics N and NFL _ew . It follows from the definitional equivalence of these systems that constructive logic with strong negation is a substructural logic. Presented by Heinrich Wansing     

The effect of sample duration and cue on a double temporal discrimination

To test the assumptions of two models of timing, Scalar Expectancy Theory (SET) and Learning to Time (LeT), nine pigeons were exposed to two temporal discriminations, each signaled by a different cue. On half of the trials, pigeons learned to choose a red key after a 1.5-s horizontal bar and a green key after a 6-s horizontal bar; on the other half of the trials, they learned to choose a blue key after a 6-s vertical bar and a yellow key after a 24-s vertical bar. During subsequent test trials, they were exposed to the horizontal or vertical bar, for durations ranging from 1.5 to 24 s, and given a choice between novel key combinations: red vs. yellow, or green vs. blue. Results showed a strong effect of sample duration—as the test signal duration increased, preference for green over blue increased and preference for red over yellow decreased. The effect of sample cue was obtained only on the green-blue test trials. These effects are discussed in light of SET and LeT.     

模态系统的推理规则的强弱虚实

模态系统的推理规则可以用强弱虚实这四种性质进行分类。在一个系统中这几种性质无论在语形上还是语义上都有一定的联系和区别,有些性质在一个系统的变种或扩充中并不一定保持。     

Products of Modal Logics. Part 3: Products of Modal and Temporal Logics

In this paper we improve the results of [2] by proving the product f.m.p. for the product of minimal n-modal and minimal n-temporal logic. For this case we modify the finite depth method introduced in [1]. The main result is applied to identify new fragments of classical first-order logic and of the equational theory of relation algebras, that are decidable and have the finite model property.     

Combinations of Tense and Modality for Predicate Logic

In recent years combinations of tense and modality have moved into the focus of logical research. From a philosophical point of view, logical systems combining tense and modality are of interest because these logics have a wide field of application in original philosophical issues, for example in the theory of causation, of action, etc. But until now only methods yielding completeness results for propositional languages have been developed. In view of philosophical applications, analogous results with respect to languages of predicate logic are desirable, and in this paper I present two such results. The main developments in this area can be split into two directions, differing in the question whether the ordering of time is world-independent or not. Semantically, this difference appears in the discussion whether T×W-frames or Kamp-frames (resp. Ockham-frames) provide a suitable semantics for combinations of tense and modality. Here, two calculi are presented, the first adequate with respect to Kamp-semantics, the second to T×W-semantics. (Both calculi contain an appropriate version of Gabbay's irreflexivity rule.) Furthermore, the proposed constructions of canonical frames simplify some of those which have hitherto been discussed.