TU Wien:Einführung in wissensbasierte Systeme VU (Egly)/Zusammenfassung

The university of Bozen-Bolzano has some nice slides (which are easier to understand than the TU slides).

First-order logic (predicate logic, PL1)

video1, video2, video3

A signature Σ lists and describes the non-logical symbols of a formal language.

A signature can be defined as a set of function symbols (and their arity) and a set of predicate symbols (and their arity).

For example: $\Sigma =\{\{a/0,b/0,\circ /2\},\{</2\}\}$

Each occurrence of a variable $x$ that is in the scope of a quantifier expression $\mathrm{\forall }x$ or $\mathrm{\exists }x$ is said to be bound. An occurrence of $x$ that is not bound is said to be free.

Formulas without free vars are called closed or sentences.

A Σ-formula is cleansed if

1. no variable has free and bound occurences, and
2. every quantifier binds a different variable

Every Σ-formula can be cleansed.

An interpretation (or Σ-structure) $ℐ$ is a triple $⟨𝒰,I,\alpha ⟩$, where

• $𝒰$ is the domain, i.e. a nonempty set of symbols
• $I(\cdot )$ is the interpretation function
• $\alpha$ is a variable assignment

An interpretation in which a formula is true is called a model for the formula.

Entailment

The formula $\varphi$ is logically implied by a formula $\psi$, if $\varphi$ is true in all models of $\psi$ (symbolically, $\psi \models \varphi$).

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Nonmonotonic reasoning

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Answer-set programming

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Probabilistic reasoning

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Good explanation on determining conditional independence based on graphical Bayes networks