Unit 7 3 First Order Logic knowitvideos Japanese English

Unit 7 3 First Order LogicYouTube↗ IA↗(long shot)
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では一階述語論理と今までに見てきた確率論や命題論理との関係について見ていきましょう

[Norvig] I'm going to talk about first order logic and its relation to the other logics we've seen so far-- namely, propositional logic and probability theory.

これらの論理体系がどのように世界を記述するのかを説明します

We're going to talk about them in terms of what they say about the world,

つまりそれらの論理の存在論的な役割と

which we call the ontological commitment of these logics,

エージェントがそれらの論理に基づいてどのような確信を得られるのかということです

and what types of beliefs agents can have using these logics,

認識論的な役割という観点から説明します

which we call the epistemological commitments.

一階述語論理では世界に存在するものや物体やそれに対する関数を表現することが可能で

So in first order logic we have relations about things in the world, objects, and functions on those objects.

それらの関係について真か偽か不明かということも表現できます

And what we can believe about those relations is that they're true or false or unknown.

これは命題論理の拡張と言えます

So this is an extension of propositional logic

命題論理では世界に存在する事実と真偽のみを扱えました

in which all we had was facts about the world and we could believe that those facts were true or false or unknown.

確率論では命題論理と同様に事実を取り扱うことができますが

In probability theory we had the same types of facts as in propositional logic--

それらに対する確信度は 0から1までの実数で表現されていました

the symbols or variables--but the beliefs could be a real number in the range 0 to 1.

このように論理によってその世界について何が言えるか

So logics vary both in what you can say about the world

そこからどのような確信を得ることができるかは異なります

and what you can believe about what's been said about the world.

知識表現について別の角度から見てみると

Another way to look at representation

世界をどのように分解して表現に落とすかというものがあります

is to break the world up into representations that are atomic,

極小な単位に分解するというのは状態をそれ以上分けられない

meaning that a representation of the state is just an individual state

独立なものに分けていくことを意味します

with no pieces inside of it.

これは探索や問題解決に用いられました

And that's what we used for search and problem solving.

Aという状態がありそこからBに遷移したとすると

We had a state, like state A, and then we transitioned to another state, like state B,

状態に対して言及できることはそれらの状態が同じものであったかどうかや

and all we could say about those states was are they identical to each other or not

それらのいずれかが目標状態だったかどうかだけです

and maybe is one of them a goal state or not.

これらの状態に内部的な構造はありません

But there wasn't any internal structure to those states.

命題論理や確率論では

In propositional logic, as well as in probability theory,

世界を真か偽で表される要因に分解し

we break up the world into a set of facts that are true or false,

これを因子表現と呼びます

so we call this a factored representation--

これは世界のそれぞれの状態がいくつかの変数

that is, the representation of an individual state of the world

例えばB、E、A、M、Jによって因子付けられ

is factored into several variables--the B and E and A and M and J, for example--

それらはブール値やそれ以外の種類の値を取るようになります

and those could be Boolean variables or in some types of representations-- not in propositional logic--they can be other types of variables besides Boolean.

第3の種類である最も複雑な知識表現は構造化です

Then the third type--the most complex type of representation--we call structured.

構造化表現においてそれぞれの状態は単なる変数の値の集合ではなく

And in a structured representation, an individual state is not just a set of values for variables,

互いに関係を持ちます

but it can include relationships between objects,

例えば分岐構造や複数の対象の間の複雑な関係などです

a branching structure, and complex representations and relations between one object and another.

これらは既存のプログラミング言語や構造化データベース

And that's what we see in traditional programming languages, it's what we see in databases--they're called structured databases,

またはそのデータベース上の問い合わせ言語などに見られ

and we have structured query languages over those databases--

この強力な表現は一階述語論理によって実現できます

and that's a more powerful representation, and that's what we get in first order logic.

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