Description Logic

Lorem ipsum dolor sit amet, consectetur adipiscing elit, sed do eiusmod tempor incididunt ut labore et dolore magna aliqua.

1. Why adding such definitions in OWL? How to know them?

• We expect the vocabulary definition language should have following features:
  1. Easy to use and understand
  2. Formal representation
  3. Sufficient expressive ability
  4. Support automated reasoning (decidable with suitable complexity)

2. Propositional Logic

2.1 Proposition

2.1.1 Def

• A Proposition is a statement which has truth value: it is either true (T) or false (F).

• 可以判断对错的陈述句

2.1.2 Example

• Which of the following are propositions?
  • 17 + 25 = 42 (√)
  • July 4 occurs in the winter in the Northern Hemisphere. (√)
  • The population of the United States is less than 250 million. (√)
  • Is the moon round (√)

2.2 Propositional Logic

2.2.1 Def:

• deals with propositions (which can be true or false) and relations between propositions, including the construction of arguments based on them.
• 即处理命题以及命题之间的关系。

2.2.2 multiple statements with logical connectives

• Negation (not): ¬
• Conjunction (and): ∧ ,
• Disjunction (or): ∨,
• Material implication (if…then): → ,
• Biconditional (if and only if): ↔ .

2.2.3 Example

• If it is sunny outside then I walk to work; otherwise I drive, and if it is raining then I carry my umbrella.

  • p = “If it is sunny outside”
  • q = “I work to work”
  • r =“I drive”
  • s = “It is raining”
  • t = “I carry my umbrella”

• If p then q; otherwise r and if s then t.

• If p then q and (if not p then (r and (if s then t))).
• (p → q) ∧ (¬ ¬ p →(r ∧ (s → t)))

2.2.4 Rule Reasoning: Modus Ponens 推理三段式