Logic

• Logic is a formal system in which the formulas or sentences have true or false values
  
  
• A logic includes:
  
  
  • Syntax: Specifies the symbols in the language and how they can be combined to form sentences. Hence facts about the world are represented as sentences in logic
    
    
  • Semantics: Specifies what facts in the world a sentence refers to. Hence, also specifies how you assign a truth value to a sentence based on its meaning in the world. A fact is a claim about the world, and may be true or false.
    
    
  • Inference Procedure: Mechanical method for computing (deriving) new (true) sentences from existing sentences
    
    
• Facts are claims about the world that are True or False, whereas a representation is an expression (sentence) in some language that can be encoded in a computer program and stands for the objects and relations in the world
  
  
• We need to ensure that the representation is consistent with reality, so that the following figure holds:
  
  

                                 entails
  Representation:    Sentences --------------> Sentences
  		       |                         |
  		       |                         |
  		       | Semantics               | Semantics
  		       | refer to                | refer to
  		       |                         |
                         \/      follows           \/
  World:               Facts ------------------> Facts
  

• Truth: A sentence is True if the state of affairs it describes is actually the case in the world. So, truth can only be assessed with respect to the semantics. Yet the computer does not know the semantics of the knowledge representation language, so we need some way of performing inferences to derive valid conclusions even when the computer does not know what the semantics (the interpretation) is
  
  
• To build a logic-based representation:
  
  
  • User defines a set of primitive symbols and the associated semantics
    
    
  • Logic defines the ways of putting these symbols together so that the user can define legal sentences in the language that represent true facts in the world
    
    
  • Logic defines ways of inferring new sentences from existing ones