## Balls and Strings: Simulations and Theories.

c-fcs-98-99

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[abstract]
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# Overview of interactions

1 9.1  Michael Thielscher
9.1  Graham White
9.1  Erik Sandewall
9.1  Graham White
9.1  A workshop participant
9.1  Graham White
2 9.1  François Lévy
9.1  Graham White

3 9.1  Pat Hayes
9.1  Graham White

4 9.1  Michael Thielscher
9.1  Graham White
9.1  Michael Thielscher
9.1  Graham White
9.1  Michael Thielscher
9.1  Graham White
9.1  Pat Hayes
9.1  Graham White

Q1. Michael Thielscher:

We have done similar things in first-order logic. What is the advantage of switching to linear logic?

A1. Graham White:

It provides a more elegant meta-theory.

C1-1. Erik Sandewall:

What is the advantage of having a more elegant meta-theory?

C1-2. Graham White:

It provides more elaboration tolerance and more modularity.

C1-3. A workshop participant:

Is any publication available which demonstrates those advantages?

C1-4. Graham White:

No, not yet.

Q2. François Lévy:

If I were convinced by your arguments and wanted to use linear logic for an application, how do I use the connectives of linear logic to describe the world?

A2. Graham White:

It is very simple, $\otimes$ for forming situations and $\multimap$ for rewrites.

Notation: $\otimes$ is the circle with an inscribed cross; $\multimap$ looks a bit like -o, that is, it is a rightward arrow but ending in a circle.

Q3. Pat Hayes:

What about if you wish to reason in different directions, and not only in the direction of the simulation, does linear logic do that?

A3. Graham White:

Yes. (Details not recorded).

Q4. Michael Thielscher:

This is important, I want to make sure I get it right. Is it the case that I can do reasoning with incomplete information about the initial state and reasoning backwards in time, using the same axioms describing the application and the same deductive procedure, if I use linear logic?

A4. Graham White:

Yes, using Girard's fixpoint theorem you can do it.

C4-1. Michael Thielscher:

Is that standard linear logic?

C4-2. Graham White:

Well, it's second order linear logic.

C4-3. Michael Thielscher:

What is the advantage of second order linear logic over first order predicate logic?

C4-4. Graham White:

I prefer the semantics.

C4-5. Pat Hayes:

What is the semantics?

C4-6. Graham White:

It is based on sets of states in Petri nets. (The discussion continued).

This on-line debate page is part of a discussion at recent workshop; similar pages are set up for each of the workshop articles. The discussion is organized by the area Reasoning about Actions and Change within the Electronic Transactions on Artificial Intelligence (ETAI).

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