Speak your mind and I will make it right: the case of “selection task”

ABSTRACT

The “Wason selection task” is still one of the most studied tasks in cognitive psychology. We argue that the low performance originally obtained seems to be caused by how the information of the task is presented. By systematically manipulating the task instructions, making explicit the information that participants are required to infer in accordance with the logical interpretation of the material implication “if, then”, we found an improvement in performance. In Experiment 1, the conditional rule has been formulated within a relevant context and in accordance with the conversational rules of communication, hence transmitting the actual meaning of the material implication. In Experiment 2, a similar improvement has been obtained even without the realistic scenario, only by making explicit the unidirectionality of the material implication. We conclude that task instructions are often formulate neglecting the conversational rules of communication, and this greatly reduces the possibility to succeed in the task.     

Quantifying definitional relations in psychological measurement

Quantitative inferences about psychological attributes, such as extraversion, depression and empathy, involve measurement instruments as well as mathematical models that specify how indicators should be aggregated. The type of model that is appropriate for doing so is conditional on the type of relation that exists between an attribute, its facets and its indicators. The common assumption is that such relations are causal relations. Here, instead, we address definitional attribute-facet relations. Our aim is to find an appropriate mathematical model for when an attribute is defined in terms of facets, instead of causing or being caused by facets. In doing so, we describe the semantics of definitions in logical form. From this form we then derive continuous functions for attribute-facet relations using fuzzy logic. A model with main effects and interactions between facets seems to be more powerful for representing definitional relations than traditional formative and reflective models. This has important implications for measurement in basic and applied research.     

Conditionals and inferential connections: toward a new semantics*

Abstract

In previous published research (“Conditionals and Inferential Connections: A Hypothetical Inferential Theory,” Cognitive Psychology, 2018), we investigated experimentally what role the presence and strength of an inferential connection between a conditional’s antecedent and consequent plays in how people process that conditional. Our analysis showed the strength of that connection to be strongly predictive of whether participants evaluated the conditional as true, false, or neither true nor false. In this article, we re-analyse the data from our previous research, now focussing on the semantics of conditionals rather than on how they are processed. Specifically, we use those data to compare the main extant semantics with each other and with inferentialism, a semantics according to which the truth of a conditional requires the presence of an inferential connection between the conditional’s component parts.     

A cirquent calculus system with clustering and ranking

Cirquent calculus is a new proof-theoretic and semantic approach introduced by G. Japaridze for the needs of his theory of computability logic (CoL). The earlier article “From formulas to cirquents in computability logic” by Japaridze generalized formulas in CoL to circuit-style structures termed cirquents. It showed that, through cirquents with what are termed clustering and ranking, one can capture, refine and generalize independence-friendly (IF) logic. Specifically, the approach allows us to account for independence from propositional connectives in the same spirit as IF logic accounts for independence from quantifiers. Japaridze's treatment of IF logic, however, was purely semantical, and no deductive system was proposed. The present paper syntactically constructs a cirquent calculus system with clustering and ranking, sound and complete w.r.t. the propositional fragment of cirquent-based semantics. Such a system captures the propositional version of what is called extended IF logic, thus being an axiomatization of a nontrivial fragment of that logic.     

A Gricean Interpretation of Nāgārjuna’s Catuṣkoṭi and the No-Thesis View

Nāgārjuna (c. 150–250 CE), the famous founder of the Madhyamika School, proposed the positive catu?ko?i in his seminal work, Mūlamadhyamakakārikā: ‘All is real, or all is unreal, all is both real and unreal, all is neither unreal nor real; this is the graded teaching of the Buddha’. He also proposed the negative catu?ko?i: ‘“It is empty” is not to be said, nor “It is non-empty,” nor that it is both, nor that it is neither; [“empty”] is said only for the sake of instruction’ and the no-thesis view: ‘No dharma whatsoever was ever taught by the Buddha to anyone’. In this essay, I adopt Gricean pragmatics to explain the positive and negative catu?ko?i and the no-thesis view proposed by Nāgārjuna in a way that does not violate classical logic. For Nāgārjuna, all statements are false as long as the hearer understands them within a reified conceptual scheme, according to which (a) substance is a basic categorical concept; (b) substances have svabhāva, and (c) names and sentences have svabhāva.     

Translation of first order formulas into ground formulas via a completion theory

A translation technique is presented which transforms a class of First Order Logic formulas, called Restricted formulas, into ground formulas. For the formulas in this class the range of quantified variables is restricted by Domain formulas.If we have a complete knowledge of the predicates involved in the Domain formulas their extensions can be evaluated with the Relational Algebra and these extensions are used to transform universal (respectively existential) quantifiers into finite conjunctions (respectively disjunctions).It is assumed that the complete knowledge is represented by Completion Axioms and Unique Name Axioms à la Reiter. These axioms involve the equality predicate. However, the translation allows to remove the equality in the ground formulas and for a large class of formulas their consequences are the same as the initial First Order formulas. This result open the door for the design of efficient deduction techniques.     

Measuring inaccuracy of uncertain doxastic states in many-valued logical systems

I will propose an alternative philosophical approach to the representation of uncertain doxastic states. I will argue that the current account of measuring inaccuracy of uncertain doxastic states is inadequate for Belnap's four-valued logic. Specifically, a situation can be found in which either an inaccuracy measure returns a completely wrong result or an agent's inaccuracy score is inadequate relative to the mistake in her doxastic attitude. This will motivate an alternative representation of uncertain doxastic states based on ordered pairs. I will describe a possible inaccuracy measure that is suitable for ordered pairs, and I will show that it has all the qualities that are required for an inaccuracy measure to be legitimate. Finally, I will introduce conditions of rationality for uncertain doxastic states represented by ordered pairs.     

Lakatos's criticism of Carnapian inductive logic was mistaken

In [39], Imre Lakatos influentially argued that Carnapian inductive logic was a degenerate research programme. This paper argues that Lakatos's criticism was mistaken and that, according to Lakatos's own standards, Carnapian inductive logic was progressive rather than degenerate.     

Formalization of Reliability Block Diagrams in Higher-order Logic

Reliability Block Diagrams (RBDs) allow us to model the failure relationships of complex systems and their sub-components and are extensively used for system reliability, availability and maintainability analyses. Traditionally, these RBD-based analyses are done using paper-and-pencil proofs or computer simulations, which cannot ascertain absolute correctness due to their inaccuracy limitations. As a complementary approach, we propose to use the higher-order logic theorem prover HOL to conduct RBD-based analysis. For this purpose, we present a higher-order logic formalization of commonly used RBD configurations, such as series, parallel, parallel-series and series-parallel, and the formal verification of their equivalent mathematical expressions. A distinguishing feature of the proposed RBD formalization is the ability to model nested RBD configurations, which are RBDs having blocks that also represent RBD configurations. This generality allows us to formally analyze the reliability of many real-world systems. For illustration purposes, we formally analyze the reliability of a generic Virtual Data Center (VDC) in a cloud computing infrastructure exhibiting the nested series-parallel RBD configuration.     

反向对抗逻辑范式的创立与证实——人工语法PDP对抗逻辑的改进

人工语法对抗逻辑范式不能排除相似性和辨别力,导致自动反应不纯粹甚至虚假或无法检测到。本研究创立反向对抗逻辑范式,采用单因素(相容/对抗条件)被试间设计:内隐学习阶段将肯定标签与语法A绑定,否定标签与语法B绑定;测量阶段相容条件组对语法A和B做与学习阶段一致的判断,对抗条件组对语法B做与学习阶段对抗的肯定判断。实验证明:(1)外显否定标签可与语法B绑定学习而获得自动化特征,产生内隐联结自动化。(2)内隐否定知识比肯定知识更自动,知识从肯定转为否定易,从否定转为肯定难。(3)反向对抗逻辑范式能有效检测到自动反应,不受语法间形式相似性和辨别力影响。(4)首次析出高概率判断偏向效应,得到纯粹受控反应。