Table of Contents

1 Reference

2 Syntax

  • the varaible starts with Upper case or underscore
    • lower case means string literal
    • underscore means anonymous varaible
  • functor must be followed directly by brace, no space
    • foo(a) foo (a)
  • ends with dot(.)

2.1 Control

maxlist([], 0).
maxlist([H|T],Max) :- maxlist(T,MaxT), (H>MaxT -> Max is H ; Max is MaxT).

If combined with other clauses, the parenthesis is must.

2.2 IS

If you want to use the inference feature, you cannot use the = or == to do equivalent checking. Instead, use the OutputVar is Something.

3 Emacs

  • C-c C-c r: eval region

4 library

5 Logic Theory

5.1 Precision and Recall

Scenario: there are a set of correct and incorrect items, we want to retrieve all the correct ones.

  • Precision: \(\frac{\text{retrieve correct}}{\text{all retrieve}}\)
  • Recall: \(\frac{\text{retrieve correct}}{\text{all correct}}\)

5.2 Syllogism (syllogistic reasoning)

  • a kind of logical argument that applies deductive reasoning to arrive at a conclusion based on two or more propositions that are asserted or assumed to be true.
  • Example
    • P1: All men are mortal.
    • P2: Socrates is a man.
    • Conclusion: Therefore Socrates is mortal.

5.3 Propositional Logic

  • proposition: a statement or assertion that express a judgement
  • Format:
    • Premise 1: \(P \rightarrow Q\)
    • Premise 2: \(P\)
    • Conclusion: \(Q\)
  • Examples
    • Premise 1: If it's raining then it's cloudy.
    • Premise 2: It's raining.
    • Conclusion: It's cloudy.

5.4 First order logic

  • Definition
    • Use Qualifiers
      • for all
      • there exists
    • Can Use Variables
  • Example
    • Propositional Logic: Socrates is a man
    • First Order Logic: there exists X such that X is Socrates and X is a man
      • \(\exists X (X \in Socrates) \cup (X \in man)\)

5.5 High order logic

  • first order logic + additional qualifiers
  • Nested qualifiers
    • \(\forall x(\exists y((f(x)=y)\land(\neg(g(y)=y))))\)

5.6 Horn Clause

  • clause is a disjunction of many predicates.
  • horn clause is a clause with at most one positive literal
  • dual-horn clause is a clause with at most one negated literal
  • definite clause is a horn clause with exactly one positive literal
    • if they all hold, then it holds
  • fact is a definite clause with no negative literal (i.e. it only has one literal)
    • assume it holds
  • goal clause is a horn clause without positive literal
    • show everyone holds