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Force-System Resultants and Equilibrium
Published in Richard C. Dorf, The Engineering Handbook, 2018
Mathematical proofs of program properties are based on a formal description of program behavior. A description of program behavior is also known as the semantics of a programming language. There are several approaches to formal semantics. Operational semantics [40] models a computation as a step-bystep process in which commands are executed one after the other. The execution process is modeled on a mathematical, high-level representation of the bits and bytes in an actual computer. Denotational semantics [34] formalizes a program as simply its input-output behavior, that is, in the simplest case, how it maps an initial state to a final state. Axiomatic semantics [25] specifies relationships between program states, such as if a predicate is true of a state, then after executing a command, a somewhat different predicate is true of the next state. Once a formal semantics is in place, we have a foundation for mathematical reasoning about programs. The properties we want to prove must also be stated formally.
Partial quasi-metrics and fixed point theory: an aggregation viewpoint
Published in International Journal of General Systems, 2021
Pilar Fuster-Parra, Juan José Miñana, Óscar Valero
In denotational semantics, one of the targets is to verify the correctness of recursive algorithms through mathematical models. With this aim, Matthews introduced the Baire partial metric space which consists of the pair , where is the set of finite and infinite sequences over a nonempty alphabet Σ and the partial metric is given by for all with denoting the longest common prefix of the words v and w when it exists and otherwise. Of course the convention that is adopted (see Matthews (1994)).
Flow semantics for intellectual control in IoT systems
Published in Journal of Decision Systems, 2018
Richard C. Linger, Alan R. Hevner
This approach offers important advantages. It requires for dependable operation that the Uncertainty Factors of the IoT environment be explicitly dealt with in flow design. It permits reasoning about flows to be localised yet complete. And it permits flows to be defined by simple deterministic structures despite the underlying asynchronous behaviour of their constituent services. These deterministic structures can be refined, abstracted, and verified using straightforward compositional methods for human understanding and intellectual control. These IoT objectives require extension of the traditional functional semantics model of programming. That model is based on denotational semantics (Stoy, 1977) and the well-known concept of programmes as rules for mathematical functions or relations, that is, mappings from domains to ranges, or stimuli to responses, as specified by transition functions (Linger, Mills, & Witt, 1979; Mills, Linger, & Hevner, 1986).
Nearness as context-dependent expression: an integrative review of modeling, measurement and contextual properties
Published in Spatial Cognition & Computation, 2020
Marc Novel, Rolf Grütter, Harold Boley, Abraham Bernstein
In section 4 we describe the concept of “nearness” and introduce the English locative “near” and identify its properties. These properties, in turn, show which requirements a model needs to meet, in order to be considered to be cognitively adequate. We also describe how “near” is ambiguous, as “near” can be used for spatial descriptions or object identification (spatial reference). We discuss a denotational semantics for the two interpretations of “near”: “near as a region” and “near as a distance”. Additionally, we discuss the pragmatic effect of functional relations.