Revising basic theorem proving algorithms to cope with the logic of partial functions

Jones, Cliff B.; Lovert, Matthew J.; Steggles, LJ

doi:10.1016/j.scico.2013.09.007

Cited by 1 publication

(1 citation statement)

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“…The initial concept was created by Łukasiewicz [32] and developed further by different logicians, such as Kleene [26], introducing the concept of "undefined" dealing with partial recursive functions. A similar concept has been later used by Jones et al in [4,24]. The three-valued approach is used in [25] for the definition of a new abstraction method for fully probabilistic systems and in [40] for model checking of Discrete-Time Markov Chains.…”

Section: Related Workmentioning

confidence: 99%

Analysis of Spatio-temporal Properties of Stochastic Systems Using TSTL

Vissat

Loreti

Nenzi

et al. 2019

ACM Trans. Model. Comput. Simul.

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In this article, we present Three-Valued spatio-temporal Logic (TSTL), which enriches the available spatiotemporal analysis of properties expressed in Signal spatio-temporal Logic (SSTL), to give further insight into the dynamic behavior of systems. Our novel analysis starts from the estimation of satisfaction probabilities of given SSTL properties and allows the analysis of their temporal and spatial evolution. Moreover, in our verification procedure, we use a three-valued approach to include the intrinsic and unavoidable uncertainty related to the simulation-based statistical evaluation of the estimates; this can be also used to assess the appropriate number of simulations to use depending on the analysis needs. We present the syntax and three-valued semantics of TSTL and specific extended monitoring algorithms to check the validity of TSTL formulas. We introduce a reliability requirement for TSTL monitoring and an automatic procedure to verify it. Two case studies demonstrate how TSTL broadens the application of spatio-temporal logics in realistic scenarios, enabling analysis of threat monitoring and privacy preservation based on spatial stochastic population models.

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