An online session of the Algebra and Logic Seminar will be held on **December 3, 2021** (Friday) at which two talks will be delivered.

**At 1:00 pm (UTC+2) **a talk on

**A Separation Theorem for Discrete Time Interval Temporal Logic**

**A Separation Theorem for Discrete Time Interval Temporal Logic**

will be delivered by **Dimitar Guelev *(joint work with Ben Moszkowski)**.

The talk will be delivered in Bulgarian with presentation in English.

**Abstract. **Gabbay’s separation theorem about linear temporal logic with past is admittedly one of the most useful theoretical results in temporal logic. In this talk, we establish an analogous statement about Moszkowski’s discrete time propositional Interval Temporal Logic (ITL) with two sets of expanding modalities, namely the unary neighbourhood modalities and the binary weak inverses of ITL’s chop operator. (The two pairs of expanding modalities are interexpressible.) We prove that separation holds for ITL both with and without its loop construct chop-star. A considerable share of these applications can be upgraded to the new case of ITL. We give brief preliminaries on ITL and LTL, and the relevance of separation to applications as known about LTL first.

**At 1:30 pm (UTC+2)** a talk on

## Restricted Quantification in New Type-Theory of Algorithms

will be delivered by **Roussanka Loukanova.**

**Abstract**. In this talk, I present an extended Type-Theory of Algorithms for restricted computations. The restrictor operator supports algorithmic rules of introduction and elimination, for each of the existential and universal quantifiers. I define and discuss new rules of existential quantification.

My focus is on development of mathematics of Type Theory, from the perspective of new, advanced technological applications. I shall point to one of its most important applications for representing semantic underspecification of quantifier scope.

The seminar will be held via Zoom and everyone can join at:

https://us02web.zoom.us/j/85137375021?pwd=RE5QczdFTE1xL1R6MnI2b1lkcGczQT09

Topic: Онлайн семинар на секция “Алгебра и логика”

Time: Dec 03, 2021 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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