Terms

• knowing/knowledge - facts and rules
• knowledge base - a collection of sentences or representations of facts about the world
• background knowledge - initial knowledge base
• sentence
  • an individual representation, expressed in a language called knowledge representation language
  • types of sentences:
    • valid
      • a sentence is valid iff it is true in all possible interpretations and all possible worlds
      • also called
        • necessarily true sentence
        • analytic sentences
        • tautologies
    • satisfiable
      • a sentence is satisfiable iff it is true in some interpretation in some world
    • unsatisfiable
      • a sentence is unsatisfiable iff it is never true in any interpretation in any world

A Knowledge-Based Agent

• a knowledge-based agent can be described in 3 levels:
  • knowledge level or epistemological level - the most abstract level of what it knows
  • logical level - the level which knowledge is encoded into sentences
  • implementation level - the level which there are physical representations of sentences

Knowledge Representation Language & Reasoning - Logic

• Knowledge Representation Language
  • the goal is to express facts in computer-tractable form
  • knowledge representation language is defined by 2 aspects
    • syntax - physical patterns stored in computer
    • semantics - the meaning of syntax
  • difference between facts and their representations
    • reasoning mechanisms must operate on representations of facts rather than facts themselves
  • types of languages
    • languages used for knowledge representation (an agent’s internal knowledge)
    • languages used for communication with other agents (such as natural languages)
  • a good knowledge representation language should combine the advantages of natural and formal languages
  • semantics
    • a sentence does not mean something by itself
    • most languages are compositional - the meaning of sentences is a function of the meaning of its parts
• Reasoning or Inference
  • reasoning/inference - the process of reaching to a conclusion
    • logical inference or deduction - sound reasoning
  • entailment - the generation of valid sentences, given background knowledge base
  • inference procedure - the steps to derive a sentence a from knowledge base
  • proof - the record of operation of a sound inference procedure
  • complete inference procedure - the ability to find a proof for any sentence that is entailed
• Logic
  • logic consists of 2 things
    • a formal system for describing states of affairs, consisting of:
      • syntax of the language - which describes how to make sentences
      • semantics of the language - which states the systematic constraints on how sentences relate to states of affairs
    • the proof theory - a set of rules for deducing the entailments of a set of sentences
  • properties of logic:
    • monotonicity - logic is monotonic, if KB1 ⊨ a then (KB1 ∪ KB2) ⊨ a
  • kinds of logic:

Propositional Logic