First-Order Dynamic Logic

Harel, David

doi:10.1007/3-540-09237-4

Cited by 427 publications

(19 citation statements)

References 48 publications

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“…Then the reduction axioms of DEL can be proven as follows. (The reduction via ∧ goes since ∀ R e † preserves meets, just the same way as in (19); the case of ¬ is similar to (20), albeit more complicated.) 26.…”

Section: Dynamic Epistemic Logicmentioning

confidence: 96%

“…• Rel is "locally posetal": For each pair of sets X and Y , the set Rel(X ,Y ) of relations from X to Y is a poset ordered by ⊆. That is, relations R 1 , R 2 : X → Y satisfy the "higher" relation R 1 ⊆ R 2 if 2 A first-order extension of dynamic logic was given in [20]. The first attempt to extend DEL to the first order was [29], which introduced terms that referred to epistemic agents (and hence had a different format of logic than in this paper).…”

Section: The Category Of Relationsmentioning

confidence: 99%

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Categories for Dynamic Epistemic Logic

Kishida

2017

Electron. Proc. Theor. Comput. Sci.

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The primary goal of this paper is to recast the semantics of modal logic, and dynamic epistemic logic (DEL) in particular, in category-theoretic terms. We first review the category of relations and categories of Kripke frames, with particular emphasis on the duality between relations and adjoint homomorphisms. Using these categories, we then reformulate the semantics of DEL in a more categorical and algebraic form. Several virtues of the new formulation will be demonstrated: The DEL idea of updating a model into another is captured naturally by the categorical perspectivewhich emphasizes a family of objects and structural relationships among them, as opposed to a single object and structure on it. Also, the categorical semantics of DEL can be merged straightforwardly with a standard categorical semantics for first-order logic, providing a semantics for first-order DEL.

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Section: Dynamic Epistemic Logicmentioning

confidence: 96%

Section: The Category Of Relationsmentioning

confidence: 99%

Categories for Dynamic Epistemic Logic

Kishida

2017

Electron. Proc. Theor. Comput. Sci.

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“…A proof calculus for Differential Dynamic Logic (dL) (first order dynamic logic for reals) and its temporal extension, developed by Harel (1979) and Platzer (2010) uses discrete/ differential induction on differential invariants/variants for compositional verification of HDS. The proof of calculus is complete relative to handling differential equations.…”

Section: Differential Dynamic Logics For Verification Of Continuous-vmentioning

confidence: 99%

“…Case 1: Tests for discrete dynamics Following Ferrante et al (2016), we run NuSMV (Cimatti et al, 2015) programmes of language generators resulting from our statechart decomposition (after collapsing embedded HA) against negations of CTL (Harel, 1979) formulas representing individual test objectives (criteria) to generate counter-examples that become tests covering required test criteria, thereby overcoming the limitations of directly translating statecharts as input for algorithms 1 and 2 of Ferrante et al, (2016).…”

Section: Proofmentioning

confidence: 99%

“…In Platzer (2010) a decomposition of hybrid systems into a sequential composition of hybrid programme (HP: their preferred MoC) components is presented; HP being extensions of conventional discrete programmes (Harel, 1979), the programmes of subsystems can be composed using logical operators in a compositional manner. However, this approach does not support parallel composition of the sequential components.…”

Section: Introductionmentioning

confidence: 99%

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Integrating runtime validation and hardware-in-the-loop (HiL) testing with V & V in complex hybrid systems

Dewasurendra

Vidanapathirana

Abeyratne

2019

J. Natn. Sci. Foundation Sri Lanka

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This study addresses the problem of assuring provably safe and correct behaviour of safety-critical complex hybrid systems (CHS) throughout their life-cycles when physical system dynamics tend to change due to natural causes. Model-based development methods are needed that integrate formal specification, verification, implementation level testing and runtime validation. Scalability limitations of available algorithms/methods dictate a modular approach, but this poses conflicting issues of compositionality, falsetransitivity, soundness and completeness. In this paper a compositional solution approach based on the decomposition and hybridisation of statechart models (into hybrid automata-HA) is demonstrated. Specifically, a compositional formal verification methodology developed earlier for discrete event dynamic systems (DEDS) was elevated to hybrid dynamics, successfully overcoming the risk of false transitivity common to direct abstraction methods of continuous state-space. It was then used to develop a scalable strategy to generate sound and complete (relative to coverage criteria) tests, and configure corresponding compositional HiL tests for different abstraction and functional levels. The same decomposition was used to derive compositional runtime validation tests based on discrete invariants and differential invariants. The study formally proves that (1) the proposed HA based formal verification method is compositional, sound and complete relative to first-order logic of differential equations, (2) the modular tests are compositional and (3) the HA based test generation method is compositional, sound and complete relative to firstorder logic of differential equations. To reduce complexity compositionality is rendered parallel than sequential to perform the simpler tasks concurrently. The claims have been validated experimentally on a full scale experimental rig.

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Time and time again: The many ways to represent time

Allen

1991

Int. J. Intell. Syst.

194

111

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One of the most crucial problems in any computer system that involves representing the world is the representation of time. This includes applications such as databases, simulation, expert systems, and applications of Artificial Intelligence in general. In this brief article, 1 will give a survey of the basic techniques available for representing time, and then talk about temporal reasoning in a general setting as needed in A1 applications. Quite different representations of time are usable depending on the assumptions that can be made about the temporal information to be represented. The most crucial issue is the degree of certainty one can assume. Can one assume that a timestamp can be assigned to each event, or barring that, that the events are fully ordered? Or can we only assume that a partial ordering of events is known? Can events be simultaneous? Can they overlap in time and yet not be simultaneous? If they are not instaneous, do we know the durations of events? Different answers to each of these questions allow very different representations of time. I. REPRESENTATIONS BASED ON DATING SCHEMESA good representation of time for instantaneous events, if it is possible, is using an absolute dating system. This involves timestamping each event with an absolute real-time, say taken off the system clock on the machine, or some other coarser-grained system such as we use for dating in everyday life. For instance, a convenient dating scheme could be a tuple consisting of the year, day in the year, hour in the day, minutes and seconds, say. For example, (1990, 110 10 4 50) would be the 110th day of 1990, at 10:04 ( A . M . ) and 50 seconds. The big advantage of dating schemes is that they provide for constant time algorithms for comparing times and use only linear space in the number of items represented. Time comparisons are reduced to simple numeric comparisons. Date-based representations are only usable, however, in applications where such information is always known, that is, applications where every

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First-Order Dynamic Logic

Cited by 427 publications

References 48 publications

Categories for Dynamic Epistemic Logic

Categories for Dynamic Epistemic Logic

Integrating runtime validation and hardware-in-the-loop (HiL) testing with V & V in complex hybrid systems

Time and time again: The many ways to represent time

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