An online session of the Algebra and Logic Seminar will be held on February 5, 2021 (Friday) at 1:00 p.m.

A talk on

will be delivered by Roussanka Loukanova, IMI – BAS.

This is a continuation of the talk given on January 29, 2021.

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

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

Topic: Онлайн семинар на секция “Алгебра и логика”
Time: Feb 05, 2021 01:00 PM Sofia
Meeting ID: 851 3737 5021
Passcode: 035647

Abstract. In 1989, Moschovakis [1] initiated a new theory of the mathematical notion of algorithm, within untyped, full recursion. In 2006, Moschovakis [2] introduced the formal language of Type-Theory of Recursion (TTR), which models the notion of algorithm and concepts of meaning in typed semantic structures. The focus of [2] is on Type-Theory of Acyclic Algorithms (TTAR) for computations that end up after a finite number of steps. The approach, in its varieties, with full and acyclic recursion, provides for new developments of type theory of computation and new applications to computational syntax-semantics interfaces in programming and natural languages.

In this talk, I present the formal language (LAR) of TTAR, by extending it with a restrictor operator that sets conditions on denotations of terms. In addition, the operator defines restricted memory and parameters. TTAR provides two kinds of semantics of the formal language LAR, denotational and algorithmic. The reduction system of TTAR is essential for the notion of algorithm and syntax-semantics interfaces. I shall overview the reduction calculus and some of the theoretical results of TTAR.

[1] Yiannis N Moschovakis. The formal language of recursion. Journal of Symbolic Logic, 54(04):1216–1252, 1989.

[2] Yiannis N. Moschovakis. A Logical Calculus of Meaning and Synonymy. Linguistics and Philosophy, 29(1):27–89, 2006.

Algebra and Logic Department, IMI-BAS
http://www.math.bas.bg/algebra/seminarAiL/