Re: [ontolog-forum] Types of Formal (logical) Definitions in ontology

[David Whitten <whitten@xxxxxxxxxx>]

Robert,

You included analogy reasoning twice. I didn't see you mention abductive reasoning.

Most people also specifically list deductive reasoning.

I notice you forgot that FOL also includes negation.

FOL and Common Logic (a superset of FOL)

both have quantifiers ForAll and ThereExists

over its Universe of Discourse.

FOL does NOT include relations & functions

in its Universe of Discourse, Common Logic does.

A lot of people differentiate modal logic, situation logic 

and temporal logic.

The basic unary (1-place) modal operators are commonly
written □ (square box) for Necessarily and ◇ (diamond)
for Possibly and ~ (tilde) for negation.

I haven't seen any specific notation for situation logic or

temporal logic. It may exist, but I haven't seen it commonly

used.

David Whitten

713-870-3834

On Wed, Jun 25, 2014 at 4:48 PM, <rrovetto@xxxxxxxxxxx> wrote:

A Summary of what's been said thus far w/follow-up Questions
- Please correct, or add, where needed. Thank you.

Aside from the links provided...

Defining mechanisms for classes (as opposed to sets)
1) An A is a B that C
- genus-species w/differentia, where differentia is some property or otherwise
2) An A is a B and a C
- conjunctive genus-species. Does this yield multiple inheritance?
3) An A is a B or a C or a ...N
- disjunctive genus-species
4) ... others?

Reasoning mechanisms distinct from (that do not use?) syllogistic logic
- induction
- analogy reasoning systems
- statistical reasoning
- calculus(?)
- "exotic mathematical methods"
- analogy-reasoning
- hybrid
-- fuzzy
- nat lang (e.g. Phil's thesis)
- @Alex: how would you call the non-fol def you originally mentioned (the VPC example)?

- neural network reasoning
- production reasoning

@Alex: You said "there are a lot of work in science and technology using FOL++ &@.

Where it does not matter how human being does thinking, but how things are."

What do you mean by 'FOL++ &@', and "[...]but how things are"? Isn't how we think one of the things that are?

JS says:
- statements about more general terms is integral to every natural language
(where nat lang is understood to be English, Spanish, etc.)

- FOL is used b/c it's considered a subset of every NL, in virtue of NL conjunctive, disjunctive and quantifier words.

- "All other logics are subsets, supersets, or variations of FOL.

Fuzzy logic, for example, assumes a continuous range of fuzzy
levels from absolutely certain (true) to absolutely not certain
(false)."

Do others agree with this last statement?
If so, does this mean that the above list are variations of FOL, which in turn is based on or contains syllogistic logic?
And does this in turn mean that all existing logics are in some part or form syllogistic?
If so, then are there possibilities for non-sylogistic logics? (in spite of the above points)

On Wed, Jun 25, 2014 at 1:07 PM, Barkmeyer, Edward J <edward.barkmeyer@xxxxxxxx> wrote:

Rich,

 

‘creative’ is not my favorite word for this kind of thing, either.  I long ago learned to distinguish ‘synthetic’ thinking from ‘analytical’ thinking, using those terms.  But I used the term ‘creative’ instead of ‘synthetic’, because Robert did, and because I don’t think of ‘creative’ thinking as “artsy”.  A popular term in my domain these days is “innovation”, which is surely a ‘creative’ process, whether the result is a new product or  a new way of accomplishing a business function or a new way of  performing a manufacturing function. 

 

BTW, neural nets have one foot in each camp.  The process that ‘trains’ the net, by establishing synaptic thresholds, is a “machine learning” process, which is in some sense synthetic.  Operating the network as a fixed structure is equivalent to the application of some (analytical) algorithm, of course, but most neural network systems also incorporate some kind of feedback mechanism from operations that is used to improve the training ‘continuously’.

 

-Ed

 

From: ontolog-forum-bounces@xxxxxxxxxxxxxxxx [mailto:ontolog-forum-bounces@xxxxxxxxxxxxxxxx] On Behalf Of Rich Cooper
Sent: Wednesday, June 25, 2014 12:24 PM

To: '[ontolog-forum] '
Subject: Re: [ontolog-forum] Types of Formal (logical) Definitions in ontology

 

Dear Ed,

 

You wrote:

 

One can argue that neural network algorithms and genetic algorithms are somehow ‘creative’ in their approach. 

 

I would prefer to use the word “productive” in the sense that these algorithms try new twists and turns that the creative human doesn’t have time to try.  But the word “creative” has always been more artsy, more squishy, not the kind of property I would attribute to neural nets at all. 

 

Genetic algorithms I would still call just “productive”; the word  “creative” doesn’t fit in the sense that only compositions of previously known genes are being embedded in the evolved creature simulation. 

 

“Creative” is different from “productive” in that the creative outcome can’t be predicted by the algorithms, as the outcomes of neural nets can be. 

 

-Rich

 

Sincerely,

Rich Cooper

EnglishLogicKernel.com

Rich AT EnglishLogicKernel DOT com

9 4 9 \ 5 2 5 - 5 7 1 2

From: ontolog-forum-bounces@xxxxxxxxxxxxxxxx [mailto:ontolog-forum-bounces@xxxxxxxxxxxxxxxx] On Behalf Of Barkmeyer, Edward J

Sent: Wednesday, June 25, 2014 8:18 AM

To: [ontolog-forum]
Subject: Re: [ontolog-forum] Types of Formal (logical) Definitions in ontology

 

Robert,

 

Assuming we take production rules engines to be ‘syllogistic reasoners’, many of them are hybrids, in the sense that they allow arbitrary Java (or LISP or other favorite programming language) functions in the ‘conditions’ in the body of a rule:  H  <- F1(x), F2(x,y)

 

As Ali mentioned, there are hybrid FOL reasoners that have built-in or plug-in function libraries for mathematical functions and geometric reasoning, and many of the Bayesian reasoners are intrinsically some kind of hybrid.  All of these approaches are, however, intrinsically deductive in their approach.  They reason from data to the consequences of the data.  The extent to which those consequences are synthetic is controlled entirely by the programmer, with a little help from the knowledge modeler (who may be one and the same).  That is to say:  the “creative” part is done by the human who creates the AI engine.

 

One can argue that neural network algorithms and genetic algorithms are somehow ‘creative’ in their approach.  Similarly systems of autonomous agents that demonstrate ‘emergent behavior’ mirror social systems of a sort – the results are not analytically predictable from the inputs.

 

Finally, there are special-purpose ‘synthesis’ technologies that generate random sentences in some “domain language” and then use statistical classification algorithms to determine the “goodness” of the generated sentences (based on expert ratings of a known sample created by humans in the domain).  I am at a total loss for references, but there were several 1980s projects in “computational music composition” that used this approach.

 

AI is a very large field.  OWL and FOL ontologies are a small garden patch.  It just happens to have a few highly visible sunflowers these days.

 

-Ed

 

From: ontolog-forum-bounces@xxxxxxxxxxxxxxxx [mailto:ontolog-forum-bounces@xxxxxxxxxxxxxxxx] On Behalf Of rrovetto@xxxxxxxxxxx

Sent: Wednesday, June 25, 2014 10:50 AM

To: [ontolog-forum]
Subject: Re: [ontolog-forum] Types of Formal (logical) Definitions in ontology

 

@Ali: Thank you. You make good points, as the other have. Wrt artificial reasoning, a hybrid or complementary reasoning system that uses non-fol and fol sounds appropriate and perhaps promising toward creativity-like and free-thinking (as you say) reasoning. Also the previous point about finding a place for fol or syllogistic logic. An unstated concern was over exclusively using a particular logic that is not enough, e.g., deduction, fol, syllogistic, to get the answers and results that the mind and scientific thought achieve. For example, many ontologies i've been exposed to use fol and I haven't seen more expressive or non-syllogstic/non-fol logics used therein. So I wonder. But if hybrid systems are making progress, great. If you have url's or pointers to some publications, i'd be curious. Thanks.

 

On Wed, Jun 25, 2014 at 10:32 AM, Ali H <asaegyn@xxxxxxxxx> wrote:

Hi Robert,

A couple of quick reactions.

 

On Wed, Jun 25, 2014 at 9:32 AM, <rrovetto@xxxxxxxxxxx> wrote:

To clarify then, I did not mean artificial languages or "method[s] of reasoning humans invent". I did not mean artificial reasoning. I meant how the mind naturally reasons.

The psychology literature (psych of reasoning I think) and elsewhere if memory serves me, demonstrates (as does our familiarity with daily interactions and inner life) that human beings do not naturally reason according to deduction (or syllgostic logic). Deduction and syllogisms leave no room for creativity which is essential. A set of premises and what follows from that. Nothing outside the box. So my question was why then use it? Why not create an artificial language that more closely approaches the truth? Even if you don't agree that our minds don't naturally employ deduction, the question "What are non-fol/non-deduction/non-syllogistic logics for ontology?" is still valid

 

But there is also a question of how you choose those premises. Are they simply static? Can you generate them dynamically? What if there is ambiguity or freedom in how you select them? What's the underlying architecture?

Admittedly, the mechanism one uses to choose (or construct) a set of premises for deductive reasoning may itself not be deductive reasoning (though you can layer multiple levels, to have a dedicated layer of FOL-based reasoning select the appropriate set of premises), but therein lies an echo to what JohnS and EdB were saying - these reasoning systems are complementary.

As an example of trying to support a creativity-like / free-thinking module, imagine you are presented with a novel set of inputs. Assuming the inputs are not already in the language of your system (though even if they are), and assuming your internal FOL system comprises of a set of FOL theories connected in a modular architecture, then there is a requisite step of mapping the inputs to your internal set of premises. This mapping process can then choose to interpret or map your input to one or more (or novel combinations) of your internal modules. But to take this further ties into your next statements:

 

But if syllogistic is used for onto's "full stop" as you said, that's troubling because of the disparity and potential issues wrt ethics and psychology.
Besides wouldn't this mean that in order to get certain answers (that beyond what deduciton or syllogisms can yeild) work-arounds, additions or corrections are needed?

If "We create ontological models of some sets of concerns, precisely because we have tools that implement syllogistic inference reliably" [bold added], then what about creating tools that implement a more realistic and expressive (closer to how our minds work) reasoning/logic?

So the other question was, what are such alternative non-deductive/non-syllogism logics that can be used for ontologies?

 

I don't see it as an either/or proposition.

One can combine the various forms of reasoning into a hybrid system (though establishing correctness for statements generated by a combination of them is not trivial). As an example, I once implemented a statement that would translate (classes of) NL statements into a HOL form, then pass it off to a physics engine + graphics processor for statistical and calculus based reasoning, before sending the results back to the HOL system for further reasoning and translation back into NL.

Having an FOL-derived base is useful as its model theory is very well known, and allows one to use it as an underlying glue to stitch together the other reasoning paradigms into a coherent and (if you're careful, in some cases) a provably consistent whole.

That said, I've found a dearth of (public?) publications on these types of hybrid reasoning systems

Best,
Ali

 

 

On Tue, Jun 24, 2014 at 5:37 PM, John F Sowa <sowa@xxxxxxxxxxx> wrote:

Ed,

I'm glad that we agree on something:

> I have a problem with: “syllogistic logic is not how the mind reasons”.
> It is rather only one of several reasoning mechanisms used by human
> minds.  We also use induction, analogy, statistical reasoning, and a
> number of exotic mathematical methods.

Every method of reasoning that humans invented is supported by the
human mind.  We don't know how to design a computer that can reason
by all the methods humans do.  But any human who designs a digital
computer or a program that runs on it knows how to reason by the
same method as the computer.

> It takes many ingredients to make the soup of human consciousness;
>  we are just growing the leeks.

I certainly agree with the first line.  But I'm not sure about
the leeks.

John

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