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Below is the fundamental axiom for Actor events (i.e. communications: ∀[S:ActorSystem, P predicateOn Event<S>] // For every ActorSystem S and every predicat
by ProfHewitt 7y ago
Below is the fundamental axiom for Actor events (i.e. communications:
∀[S:ActorSystem, P predicateOn Event<S>] // For every ActorSystem S and every predicate P on events of S
(∀[x:Primordial<S>] P[Creation[x]] // If P holds for the creation event of every primordial of S
⋀ ∀[e:FromOutside<S>] P[e] // and P holds for every event from outside S
⋀ ∀[e:Event<S>, e1:ImmediatelyFollows<e>] // and for every event of S
P[e]⇒P[e1]) // if P holds for the event, then P holds for each immediately following event
⇒ ∀[e:Event<S>] P[e] // then P holds for every event of S
See the following for more explanation: https://papers.ssrn.com/sol3/papers.cfm?abstract_id=3459566 https://papers.ssrn.com/sol3/papers.cfm?abstract_id=3459566
- elegaphant 7y agoI have an applied math background. What resources are recommend to understand the symbols used here?
- deleted 7y ago[deleted]
- trobertson 7y agoThe base notation is from formal logic. A (dense) overview of first-order logic can be found on this wikipedia page: https://en.wikipedia.org/wiki/First-order_logic https://en.wikipedia.org/wiki/First-order_logic It's much nicer to get slowly walked through it with a textbook, but I'm blanking on the name of the book I used.
- elegaphant 7y agoThanks trobertson. This may be what I need. So, may I presume that the notation of (Prof) Carl Hewitt’s Direct Logic is consistant with that of First-Order Logic?
- ProfHewitt 7y agoActually, the notation used above is for strongly-typed higher-order theories. See the following: https://papers.ssrn.com/sol3/papers.cfm?abstract_id=3418003 https://papers.ssrn.com/sol3/papers.cfm?abstract_id=3418003 https://papers.ssrn.com/sol3/papers.cfm?abstract_id=3459566 https://papers.ssrn.com/sol3/papers.cfm?abstract_id=3459566
- eindiran 7y agoHere is a free text book that covers most of the notation, except the quantifiers, around page 30 or so: https://www.textbookequity.org/Textbooks/Magnus_forallx.pdf https://www.textbookequity.org/Textbooks/Magnus_forallx.pdf For the quantifiers, check out the Wikipedia page here: https://en.m.wikipedia.org/wiki/Quantifier_(logic) https://en.m.wikipedia.org/wiki/Quantifier_(logic) For deeper coverage, the section on first order logic here is quite good: https://www.amazon.com/Introduction-Montague-Semantics-Synthese-Language/dp/9027711429 https://www.amazon.com/Introduction-Montague-Semantics-Synth...