2003
DOI: 10.1007/s00236-002-0098-z
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A functional approach for temporal $\times$ modal logics

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Cited by 5 publications
(10 citation statements)
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“…All of the previous systems are complete except S I -Surj. For the sake of simplicity, we will focus our attention on the proof of completeness of the system S I -Inj, because the corresponding system for total injective functions with non indexed connectives was proved to be incomplete in [9]. Similar proofs can be given for S I -Non-T ot, S I -Cons, S I -Str-Inc and S I -Str-Dec.…”
Section: For Eachmentioning
confidence: 99%
See 3 more Smart Citations
“…All of the previous systems are complete except S I -Surj. For the sake of simplicity, we will focus our attention on the proof of completeness of the system S I -Inj, because the corresponding system for total injective functions with non indexed connectives was proved to be incomplete in [9]. Similar proofs can be given for S I -Non-T ot, S I -Cons, S I -Str-Inc and S I -Str-Dec.…”
Section: For Eachmentioning
confidence: 99%
“…Hence, we will focus our attention on completeness. Specifically, we will provide a proof of completeness by using the step-by-step method (see, for example, [7] and [8] for modal and temporal systems, and [10] and [9] for functional systems). In this section, we consider the system S I -Inj, however easy modifications would lead us to obtain the completeness of the system for total injective functions S I -T ot-Inj 1) .…”
Section: Soundness and Completeness Of S I -Injmentioning
confidence: 99%
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“…Basically, this functional approach is based on possible worlds semantics, each world with its own (linear) temporal flow. The most significant feature of this approach is the use of functions (called accessibility functions) to connect the temporal flows in a frame, called functional frame [5][6][7]. Technically, functional frames constitute a generalization of Kamp-frames [6] by establishing more complex comparisons among different temporal flows.…”
Section: Introductionmentioning
confidence: 99%