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Graham White

Balls and Strings: Simulations and Theories.

c-fcs-98-99
 
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Overview of interactions

N:o Question Answer(s) Continued discussion
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).


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