*Zar Goertzel* wrote: > Briefly asked Chad the logic guru. > > He says sounds like the proof-logic for parsing would be something in the > linear logic direction. Mentions Lambek and > https://en.wikipedia.org/wiki/Grammatical_Framework. > But he isn't sure something as detailed/formal as you'd like has been done > yet... >
I'm exploring parsing vs. proof construction. What I've found out for now is that Hilbert system <https://en.wikipedia.org/wiki/Hilbert_system> (an analogue to OpenCog unified rule engine) is an equivalent to unrestricted grammars <https://en.wikipedia.org/wiki/Unrestricted_grammar> from Chomsky hierarchy <https://en.wikipedia.org/wiki/Chomsky_hierarchy> (Type 0). The difference is merely in notation direction where Hilbert writes rules from left to right, while parsing grammar productions reverse left and right sides. The connection is the following (using Hilbert's direction): - (cause / string-of-terminals-or-non-terminals-to-be-parsed) *->* (consequence / match-pattern) With a help of common rules (again in Hilbert System): - A *->* (A \/ B) - B *->* (A \/ B) Proving is performed from left to right, while parsing is performed from right to left. Considering Curry-Howard-Lambek <https://en.wikipedia.org/wiki/Curry%E2%80%93Howard_correspondence> correspondence, I suppose we may add unrestricted grammars to it also. Unrestricted grammars are anyway considered Turing machine equivalent <https://en.wikipedia.org/wiki/Unrestricted_grammar#Equivalence_to_Turing_machines> rewriting <https://en.wikipedia.org/wiki/Rewriting> mechanisms, so this should be no surprise at all, although I didn't imagine it would be that simple and straightforward. If anyone is interested in serious parser/proof material written by professionals, there is excellent Stanford's Introduction to Logic <http://intrologic.stanford.edu/public/index.php>. Chapter 9.6 - Pseudo English <http://intrologic.stanford.edu/public/section.php?section=section_09_06> covers a kind of context free grammars implemented in logic, and we should be able to extended it to unrestricted grammars also. Stay cool, Ivan V. pon, 17. pro 2018. u 12:32 Zar Goertzel <[email protected]> napisao je: > Briefly asked Chad the logic guru. > > He says sounds like the proof-logic for parsing would be something in the > linear logic direction. Mentions Lambek and > https://en.wikipedia.org/wiki/Grammatical_Framework. > But he isn't sure something as detailed/formal as you'd like has been done > yet... > > On Fri, Dec 14, 2018 at 12:27 PM Zar Goertzel <[email protected]> wrote: > >> Howdy Linas, >> >> Unfortunately, I'm drastically ignorant compared to my senior colleagues >> and you. >> >> Re: URE: So curry-howard says "proofs are programs" and it turns out >> that theorem proving is a lot like parsing (its identical to >> parsing???) I DO NOT know of any simple write-up of this topic; I can >> only wave my hands around. When I mentioned this to Ben's son Zar, he >> kind-of responded and said "duhh its obvious everyone knows this." >> >> Zar, do you know of any nice readable references that explain how >> theorem-proving and parsing are "the same thing"? >> >> >> We had happened to be talking about it at lunch when you brought that up. >> It seems likely they're in a similar state to you: it seems obvious and >> they can wave their hands around, but haven't bothered formally writing it >> up. >> >> Would it be hard to write up formally? >> >> On Wed, Dec 12, 2018 at 1:17 AM Linas Vepstas <[email protected]> >> wrote: >> >>> Oh, and one more (minor?) remark: the intermediate states that get >>> explored during pattern matching are called "Kripke frames", and the >>> "crisp logic of term re-writing" is one of the modal logics. I know >>> this to be true in a hand-waving fashion; I have searched long and >>> hard for a paper or a book that would articulate this in some direct, >>> detailed fashion. I have not yet found one. >>> >>> Zar, so second question, any chance at all you might be aware of >>> references for this? >>> >> >> The logic of term rewriting is paramodulation? That's not a modal logic >> though . . . >> >> >>> >>> --linas >>> On Tue, Dec 11, 2018 at 2:24 AM Ivan Vodišek <[email protected]> >>> wrote: >>> > >>> > Linas, >>> > >>> > Thank you for taking a time to response, I'll try to keep this short. >>> I might be wrong, but Curry-Howard-Lambek isomorphism inspires me greatly >>> in a pursuit for one-declarative-language-like-URE-to-rule-them-all. >>> > >>> > I see term rewriting simply as basic implication over input and output >>> terms. A number of term rewriting rules may be bundled together in a >>> conjunction. Alternate pattern-matching options may form a disjunction. And >>> pattern exclusion may be expressed as a negation. These are all common >>> logical operators in a role of defining a term rewriting system. And since >>> this kind of term rewriting is basically a logic, it can generally be >>> tested for contradiction, or it can be used for deriving relative indirect >>> rules - if we want it so. >>> > >>> > That's a short version of what I currently work on - a term rewriting >>> system expressed as a crisp logic - just a few basic logic operators with >>> no hard-wired constants other than true and false - all wrapped up in a >>> human friendly code code processor. >>> > >>> > - Ivan V. - >>> > >>> > uto, 11. pro 2018. u 04:07 Linas Vepstas <[email protected]> >>> napisao je: >>> >> >>> >> On Sun, Dec 9, 2018 at 11:55 AM Ivan Vodišek <[email protected]> >>> wrote: >>> >> > >>> >> > Oh, I see, I must be talking about URE then. All cool, then it >>> seems reasonable to me (one ring to rule them all - policy). >>> >> > >>> >> > I keep persuading myself that a perfect single declarative - logic >>> + lambda calculus + type theory exists, or could be invented, >>> >> >>> >> So, OK, the atomspace is trying to be: >>> >> >>> >> + declarative: so kind-of-like datalog or kind-of like SQL or noSQL, >>> >> or some quasi-generic (graph) data store. But you already know this. >>> >> >>> >> - it does NOT have "logic" in it, in any traditional sense of the word >>> >> "logic". It does have the ability to perform term-rewriting (pattern >>> >> re-writing, graph re-writing). >>> >> >>> >> - lambda calculus is a form of "string rewriting". Note that string >>> >> rewriting is closely related to term rewriting (but not quite the same >>> >> thing) and that term rewriting is closely related to graph rewriting >>> >> (but not quite the same thing). >>> >> >>> >> When lambda calculus was invented, any distinction between strings, >>> >> terms, and graphs was unknown and unknowable, until the basic concepts >>> >> got worked out. So, due to "historical accident", generic lambda >>> >> calculus remains a string rewriting system. As stuff got worked out >>> >> over the 20th century, the concept of "term rewriting" gelled as a >>> >> distinct concept. (And other mind-bendingly >>> >> similar-but-slightly-different ideas, like universal algebra, model >>> >> theory ... and bite my tongue. There's more that's "almost the same as >>> >> lambda calc. but not quite". A veritable ocean of closely related >>> >> ideas.) >>> >> >>> >> From practical experience with atomspace, it turns out that trying to >>> >> pretend that all three rewriting styles (string, term, graph) are the >>> >> same thing "mostly works", but causes all kinds of friction, >>> >> confusion, conundrums in detailed little corners. So, for example, >>> >> BindLink was an early attempt to define a Lambda for declarative >>> >> graphs. In many/most ways, it really is "just plain-old-lambda". It >>> >> works, and works great to this day, but, never-the-less, we also >>> >> created more stuff that is "just like lambda, but different", >>> >> including LambdaLink, etc. >>> >> >>> >> In many ways, its an ongoing experiment. The search for "perfect" has >>> >> more recently lead to "values", which are a lot like "valuations" in >>> >> model theory. (and again, recall that model-theory is kind-of-ish like >>> >> lambda-calculus, but its typed.) >>> >> >>> >> There's no "logic" in the atomspace, but you could add logic by using >>> >> the URE, and/or by several other ways, including parsing, sheaves, and >>> >> openpsi. In short, there's lots of different kinds of logic, and lots >>> >> of different ways of implementing it, and we are weakly fiddling with >>> >> several different approaches. And I have more in mind, but lacking in >>> >> time. >>> >> >>> >> -- Linas >>> >> -- >>> >> cassette tapes - analog TV - film cameras - you >>> >> >>> >> -- >>> >> You received this message because you are subscribed to the Google >>> Groups "opencog" group. >>> >> To unsubscribe from this group and stop receiving emails from it, >>> send an email to [email protected]. >>> >> To post to this group, send email to [email protected]. >>> >> Visit this group at https://groups.google.com/group/opencog. >>> >> To view this discussion on the web visit >>> https://groups.google.com/d/msgid/opencog/CAHrUA35V2Uk0YbwERPMkPhpxevriT0DZvaYzLtEPXUQC9TiUHQ%40mail.gmail.com >>> . >>> >> For more options, visit https://groups.google.com/d/optout. >>> > >>> > -- >>> > You received this message because you are subscribed to the Google >>> Groups "opencog" group. >>> > To unsubscribe from this group and stop receiving emails from it, send >>> an email to [email protected]. >>> > To post to this group, send email to [email protected]. >>> > Visit this group at https://groups.google.com/group/opencog. >>> > To view this discussion on the web visit >>> https://groups.google.com/d/msgid/opencog/CAB5%3Dj6VaDej%3DGBL3bpMxYArP6ZnkifCiNmStc7-SrJO%2BV3eHQA%40mail.gmail.com >>> . >>> > For more options, visit https://groups.google.com/d/optout. >>> >>> >>> >>> -- >>> cassette tapes - analog TV - film cameras - you >>> >> -- > You received this message because you are subscribed to the Google Groups > "opencog" group. > To unsubscribe from this group and stop receiving emails from it, send an > email to [email protected]. > To post to this group, send email to [email protected]. > Visit this group at https://groups.google.com/group/opencog. > To view this discussion on the web visit > https://groups.google.com/d/msgid/opencog/CAHY-%3DHEmBKgtJPAeKTXAOyOaE4gR8cZeouc8v9JhQb3E4jX%2BkQ%40mail.gmail.com > <https://groups.google.com/d/msgid/opencog/CAHY-%3DHEmBKgtJPAeKTXAOyOaE4gR8cZeouc8v9JhQb3E4jX%2BkQ%40mail.gmail.com?utm_medium=email&utm_source=footer> > . > For more options, visit https://groups.google.com/d/optout. > -- You received this message because you are subscribed to the Google Groups "opencog" group. 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