The next meeting of the Algebra and Logic Seminar will be held on October 21, 2022 (Friday) at 1:00 pm (UTC+2) online in Zoom.
A talk on:
Gabbay Separation for the Duration Calculus
will be delivered by Dimitar Guelev (IMI – BAS).
Abstract.
Gabbay’s separation theorem about linear temporal logic (LTL) with past has proved to be one of the most useful theoretical results in temporal logic. Is expressive power ultimately affected, if past constructs are not allowed in the scope of future ones, or vice versa? Separation implies that it does not, and also provides a technically convenient normal form for temporal conditions.
Interval Temporal Logic (ITL) and the Duration Calculus (DC) are interval-based logics. Unlike LTL, they are based on modalities which allow reference to subintervals of the reference intervals only. Adding the neighbourhood modalities, which are written <A> and <A-1> in the notation stemming from Allen’s system of interval relations, enables reference outside the reference interval and this way makes temporal separation relevant. In this talk I propose a DC analogue of a separation theorem for discrete time ITL which I established in a joint work with Ben Moszkowski.
Both theorems are analogous to Gabbay’s pioneering result and can be spelled out in similar terms, but the technical differences are significant. I take the opportunity to not repeat my previous talk on separation for ITL and instead discuss some aspects of the proofs for both the ITL and the DC theorems. Interestingly, these theorems admit proofs that are based on syntactical transformations of the formulas in the respective logics, and are therefore compositional and very intuitive. I will focus on the common and the distinct features of the proofs, and on some side corollaries.
The seminar will be held online. Join the Zoom link:
https://us02web.zoom.us/j/
Topic: Онлайн семинар на секция “Алгебра и логика”
Time: Oct 28, 2022 01:00 PM Sofia
Meeting ID: 851 3737 5021
Passcode: 035647
Algebra and Logic Department, IMI – BAS
http://www.math.bas.bg/algebra/seminarAiL/
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