Formal assessment of reliability specifications in embedded cyber-physical systems

Reliability has become an integral component of the design intent of embedded cyber-physical systems. Safety-critical embedded systems are designed with specific reliability targets, and design practices include the appropriate allocation of both spatial and temporal redundancies in the implementation to meet such requirements. With increasing complexity of such systems and considering the large number of components in such systems, redundancy allocation requires a formal scientific basis. In this work, we profess the analysis of the redundancy requirement upfront with the objective of making it an integral part of the specification. The underlying problem is one of synthesizing a formal specification with built-in redundancy artifacts, from the formal properties of the error-free system, the error probabilities of the control components, and the reliability target. We believe that upfront formal analysis of redundancy requirements is important in budgeting the resource requirements from a cost versus reliability perspective. Several case-studies from the automotive domain highlight the efficacy of our proposal.     

Reconceptualizing the Transitive Inference Ability: A Framework for Existing and Future Research

It has often been claimed that to demonstrate transitive inference is to demonstrate a logical ability, and by implication that transitivity as a property is generally a logical entity. Both claims are considered using a theoretically driven analysis together with consideration of relevant existing experimental research and some newly reported findings. This approach suggests an account of transitivity and transitive inferential reasoning that differs not only from the classic Piagetian account, but also from the information processing account so dominant today. We begin by considering one important issue, that the “logical” definitional criterion can only be approached if individuals are required to demonstrate a capacity for transitive inference that is discriminative in nature. This, together with interpretation of findings from existing transitive tasks, leads to the postulate of a three-component psychological system, with the components relying on perceptual, linguistic, and conceptual subprocesses and sensitivity to simple cues. The framework is testable and accommodates important aspects of classic and modern accounts of “transitive development” that until now have been taken to be mutually exclusive. It also readily accommodates both human and nonhuman research, yet neither a formal logical structure nor memory in any general sense need be assigned the primary role.     

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.