Lambda the Ultimate

inactiveTopic The Foundations of Two-Dimensional Semantics
started 9/29/2002; 1:27:02 PM - last post 10/3/2002; 2:19:36 AM
Ehud Lamm - The Foundations of Two-Dimensional Semantics  blueArrow
9/29/2002; 1:27:02 PM (reads: 443, responses: 2)
The Foundations of Two-Dimensional Semantics
The core idea of two-dimensional semantics is that there are two different ways in which the extension of an expression depends on possible states of the world. First, the actual extension of an expression depends on the character of the actual world in which an expression is uttered. Second, the counterfactual extension of an expression depends on the character of the counterfactual world in which the expression is evaluated. Corresponding to these two sorts of dependence, expressions correspondingly have two sorts of intensions, associating possible states of the world with extensions in different ways. On the two-dimensional framework, these two intensions can be seen as capturing two dimensions of meaning.

This is a philosophy paper, so if you are only into programming, skip to the next item.

While this paper deals with the semantics of statements in general, I have a feeling that by clarifying important notions (e.g., context and intension) it can be helpful for those doing more technical work on semantics -- and programming language semantics.

Maybe one of our semantics gods would like to comment?

Posted to general by Ehud Lamm on 9/29/02; 1:27:34 PM

jon fernquest - Re: The Foundations of Two-Dimensional Semantics  blueArrow
10/1/2002; 3:01:03 AM (reads: 444, responses: 0)
I tried to read this paper, but I blew a couple of circuits along the way....

I came across a paper not so long ago that compares the semantics of programming languages with that of natural languages and philosophy written by a linguist:

The four basic ontologies of semantic interpretation

The [-sense,+constructive] ontology (iii) is that of the semantics of programming languages. The user puts commands (surfaces of the programming language) into the computer, which turns them directly into corresponding electronic procedures. When a result has been computed, it is communicated to the user by displaying language expressions on the screen. In this traditional use, a computer is still a far cry from a cognitive agent. But there is already the important distinction between the task environment in the `world' and the computer internal problem space, whereby the semantic interpretation is located in the latter.

When I read this I thought: "What about abstractions in programming?" In the beginning of the paragraph they seem to be denying the existence of programming abstractions and at the end admitting it back in again. Maybe the simple binary distinctions they're trying to make are the problem?

To be honest, I really don't understand the paper as a whole, exactly what it is trying to achieve, or what the implications of its judgements are. I'd like to though. Anyone?

Frank Atanassow - Re: The Foundations of Two-Dimensional Semantics  blueArrow
10/3/2002; 2:19:36 AM (reads: 409, responses: 0)
My work is basically founded on higher-dimensional algebraic semantics, so this paper sounded very interesting to me, but looking at it I don't see much that I recognize. Anyway, it seems quite dense.

I will maybe have a closer look over the weekend.