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Unity Logic System

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Am trying to create a conversagent agent capable of memory and thought. Check my other thread for more details. I am after a logically capable agent who can detect contradictions or can validate conclusions according to the common laws of logic. I have been checking the Wikipedia for axioms of logic, Boolean algebra. How could I integrate these axioms into a framework to solve any problem that I might encounter. Your help is highly appreciated.

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Fortunately for you, this is an extremely well-studied area of artificial intelligence. The procedure for doing this goes something like the following diagram. Imagine that we ask the system to answer the question: "Given that all men are mortals (and that there's at least one man), are there some mortals who are men?"

{ English statements } ------+                        "All men are mortals."
|
[natural language parser]
|
|
{ logical predicates } <-----+ "∀ m | m ∈ Men &rArr m ∈ Mortals"
|
|
[inference engine]
|
+----------------> { knowledge base } "P1 = ∀ m | m ∈ Men ⇒ m ∈ Mortals"
|
|
[deductive engine]
|
|
{ draw conclusions for answer } <----+ "P1"
"P1 ⇒? (∃ m ∈ Mortals ⇒ m ∈ Men)"
∴ (∃ m | m ∈ Mortals ⇒ m ∈ Men)"
return true;


Unfortunately for you, English is an extremely ambiguous language. To avoid a very complicated system, you will probably need to bypass the natural language parser step and require your users to deal directly with logical predicates. Be warned that constructing a system to process the logical inputs and draw inferences is approximately as much work as building a compiler for a small but nontrivial language. If you want to know more, an excellent book on the subject is "Artificial Intelligence: A Modern Approach" by Russell and Norvig.

hope that helps,

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What is this little square that keeps being iterated all over, I saw it in Wikipedia, you typed it here... It is driving me insane.

As for the book you mentioned, I am away from university right now, but I will check it as soon as possible.

I was thinking about using a transformation engine with something like the A* algorithm to find whether there is, or isn't any contradictions with the acquired knowledge. I am stomped at the first step, which is which rules to use.

Till now, I am considering studying each operator {not, and, or} and creating transformation laws for any combination of those. But am still a little fuzzy about the whole thing and I still need further clarification please.

Thanks for the illustrative diagrams kSquared.

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Original post by arithma
What is this little square that keeps being iterated all over, I saw it in Wikipedia, you typed it here... It is driving me insane.

Can you be more specific? I don't see any squares in what I typed.

[edit: It might be that your browser can't render certain symbols. Can you take a screenshot of my post?]

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It seems I am missing some font packages since it cannot render the &-forall glyph.. How should I correct this?

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Original post by arithma
It seems I am missing some font packages since it cannot render the &-forall glyph.. How should I correct this?

Your browser is responsible for rendering the glyphs, not per se the fonts (your browser should be substituting things as need be, or drawing them itself).

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kSquared
Be warned that constructing a system to process the logical inputs and draw inferences is approximately as much work as building a compiler for a small but nontrivial language.


What do you exactly mean. The inference algorithm is hard or the parsing of english is hard?

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Quote:
Original post by arithma
Quote:
kSquared
Be warned that constructing a system to process the logical inputs and draw inferences is approximately as much work as building a compiler for a small but nontrivial language.


What do you exactly mean. The inference algorithm is hard or the parsing of english is hard?


Well, neither of them are easy. But parsing natural language remains a largely unsolved problem.

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I'm not sure if this is of any help to you (i usually work more in terms of chatbots then logic agents, but then again, i've been making them for quite awhile now....)

Basically what i do is that i store my kb inside a semantic net.
Now, you must be wondering, how do i convert english into something for a semantic net?

The answer is that i only allow people to use a subset of english.

For example "The box is blue"

You find the keywords. In this case, "The" and "is".

"is" is the link between "The box" and "Blue"

Now to find "The box". We look at all the box's, and we find the one that was last "touched". (ie. talked about, seen, heard).

We then have a node id for "The box".

We then find the node id for "blue".

And we then add a link from the node id of "the box" to the node id for "blue".

Now if somebody asks "What colour is the box?"

We then figure out that its a question (it starts with an interogitive)

We get rid of the interogitive. (and place it somewhere for later).

The keyword is "is".

We then find the node id for "The box".

And we then check its links of that node, for one which then links to colour.
The link for a link is used when your doing a "what ...?" search. For example, if your looking for an "is x ...?", then you simply check all links for one that matches.

In this case, it "is" blue, which then "is" a colour.

so we can then say "The box is blue".


Now for the logic....


"All men are mortal".
We can rephrase that to be
"If X is a man, then X is mortal"

Which is simple enough to search for. Look through your semantic net, for somebody that links to man.

For example, Nice coder is a man.
The node for nice coder, links using link "is" with the node for man.
So we then add a link from the node for nice coder to the node for mortal.

So now, if asked "is nice coder mortal?" it'll tell you "yes". (the node called nice coder has a link to the node called mortal).

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