Special issue: Combining probability and logic

This editorial explains the scope of the special issue and provides a thematic introduction to the contributed papers.     

The Concept of Intermediate Existence in the Early Buddhist Theory of rebirth

This article investigates the concept of intermediate existence in the early Buddhist theory of rebirth. The main sources investigated for this article are the Pāli canonical and commentarial literature. My main thesis is that early Buddhist discourses contain instances that suggest a spatial-temporal gap between death and rebirth known as ‘intermediate existence’ (antarābhava), in contrast to the idea of Theravāda Buddhist theory that rebirth takes place immediately without a spatial-temporal gap. In order to prove this, I argue that the ‘one who liberates in interval’ (anarāparinibbāyī) attains Nibbāna in the intermediate existence and the concept of gandhabbā in early Buddhist discourses refers to a being in intermediate existence, not to a dying consciousness (cuti-viññāna), and there are indirect inferences to an spatiotemporal gap between death and rebirth in the early Buddhist discourses.     

Borderline personality disorder in an intermediate psychological therapies service

The intermediate psychological therapies service is provided for individuals referred with common mental health problems within the primary care psychological therapies service, but whose difficulties are longstanding and/or complex. The prevalence of borderline personality disorder (BPD) in intermediate psychological therapy services has not been researched to-date. The current study aimed to measure the prevalence of BPD amongst patients attending intermediate psychological therapies (n?=?63). The prevalence of BPD was established by identifying the number of patients who met DSM-IV criteria. BPD prevalence amongst patients attending an intermediate psychological therapy service was 37%. The high proportion of patients presenting with BPD indicates the potential need for staff training and supervision in how to manage such high levels of need at this service level. This is the first study to report prevalence rates of BPD specifically in an intermediate care psychological therapy service.     

Combinator Logics

Combinator logics are a broad family of substructual logics that are formed by extending the basic relevant logic B with axioms that correspond closely to the reduction rules of proper combinators in combinatory logic. In the Routley-Meyer relational semantics for relevant logic each such combinator logic is characterized by the class of frames that meet a first-order condition that also directly corresponds to the same combinator's reduction rule. A second family of logics is also introduced that extends B with the addition of propositional constants that correspond to combinators. These are characterized by relational frames that meet first-order conditions that reflect the structures of the combinators themselves.     

Measuring coherence using LP-models

This paper introduces a technique for measuring the degree of (in)coherence of inconsistent sets of propositional formulas. The coherence of these sets of formulas is calculated using the minimal models of those sets in G. Priest's Logic of Paradox. The compatibility of the information expressed by a set of formulas with the background or domain knowledge can also be measured with this technique. In this way, Hunter's objections to many-valued paraconsistent logics as instruments for measuring (in)coherence are addressed.     

An analytic tableau calculus for a temporalised belief logic

A tableau is a refutation-based decision procedure for a related logic, and is among the most popular proof procedures for modal logics. In this paper, we present a labelled tableau calculus for a temporalised belief logic called TML⁺, which is obtained by adding a linear-time temporal logic onto a belief logic by the temporalisation method of Finger and Gabbay. We first establish the soundness and the completeness of the labelled tableau calculus based on the soundness and completeness results of its constituent logics. We then sketch a resolution-type proof procedure that complements the tableau calculus and also propose a model checking algorithm for TML⁺ based on the recent results for model checking procedures for temporalised logics. TML⁺ is suitable for formalising trust and agent beliefs and reasoning about their evolution for agent-based systems. Based on the logic TML⁺, the proposed labelled tableau calculus could be used for analysis, design and verification of agent-based systems operating in dynamic environments.     

首、尾语素频率对中级印尼汉语学习者复合词识别的影响

通过词汇判断任务,探讨语素频率对中级印尼汉语学习者复合词识别的影响。研究结果发现,语素频率影响中级印尼汉语学习者复合词的识别。同时,语素频率对词汇识别的影响受到语素位置的调节。当语素为复合词的首语素时,语素频率高,词汇判断的正确率高;语素频率低,词汇判断的正确率低。当语素为复合词的尾语素时,语素频率对词汇判断正确率的影响受到首语素频率的限制。只有当首语素的频率高时,尾语素的频率才会影响词汇判断的正确率。当首语素的频率低时,尾语素的频率不影响词汇判断的正确率。研究结果支持中级印尼汉语学习者在复合词的表征中产生了语素表征,而且首语素的频率在复合词识别中发挥更重要的作用。     

Proper Semantics for Substructural Logics,from a Stalker Theoretic Point of View

We study filters in residuated structures that are associated with congruence relations (which we call -filters), and develop a semantical theory for general substructural logics based on the notion of primeness for those filters. We first generalize Stone’s sheaf representation theorem to general substructural logics and then define the primeness of -filters as being “points” (or stalkers) of the space, the spectrum, on which the representing sheaf is defined. Prime FL-filters will turn out to coincide with truth sets under various well known semantics for certain substructural logics. We also investigate which structural rules are needed to interpret each connective in terms of prime -filters in the same way as in Kripke or Routley-Meyer semantics. We may consider that the set of the structural rules that each connective needs in this sense reflects the difficulty of giving the meaning of the connective. A surprising discovery is that connectives , ⅋ of linear logic are linearly ordered in terms of the difficulty in this sense. Presented by Wojciech Buszkowski     

Applied Logic without Psychologism

Logic is a celebrated representation language because of its formal generality. But there are two senses in which a logic may be considered general, one that concerns a technical ability to discriminate between different types of individuals, and another that concerns constitutive norms for reasoning as such. This essay embraces the former, permutation-invariance conception of logic and rejects the latter, Fregean conception of logic. The question of how to apply logic under this pure invariantist view is addressed, and a methodology is given. The pure invariantist view is contrasted with logical pluralism, and a methodology for applied logic is demonstrated in remarks on a variety of issues concerning non-monotonic logic and non-monotonic inference, including Charles Morgan’s impossibility results for non-monotonic logic, David Makinson’s normative constraints for non-monotonic inference, and Igor Douven and Timothy Williamson’s proposed formal constraints on rational acceptance.     

Majority merging by adaptive counting

The present paper introduces a belief merging procedure by majority using the standard format of Adaptive Logics. The core structure of the logic ADM ^c (Adaptive Doxastic Merging by Counting) consists in the formulation of the conflicts arising from the belief bases of the agents involved in the procedure. A strategy is then defined both semantically and proof-theoretically which selects the consistent contents answering to a majority principle. The results obtained are proven to be equivalent to a standard majority operator for bases with partial support.