15-815 Automated Theorem Proving

Project Week 1: Propositional Reasoning

Red Group (Inverse Method)

Green Group (Inverse Method)

Work on the inverse method in the first week focuses on establishing the basic inference mechanism, including subformula labelling and forward subsumption in the propositional case.

1 Interface: Parsing and printing of propositions (see grammar); Subterm labeling
2 Validation: Proof term calculus; Checker for proof terms
3 Search: Applying inference rules; Saturating clause space
4 Redundancy Elimination: Ordering of propositions; Forward subsumption
5 Coordination: Creating initial regression testing suite; Signature coordination; Summary progress report; Task assignment for next week

Blue Group (Backward Reasoning)

Work on the backwards method in the first week focuses on taking the implementations of backward reasoning presented in class so far and adding parsing, printing, and proof terms for the propositional case. Also, we aim to improve efficiency of loop detection via subformula labeling as in the inverse method.

1 Interface: Parsing and printing of propositions (see grammar); Subterm labeling
2 Validation: Proof term calculus; Checker for proof terms
3 Search: Applying focusing rules
4 Redundancy Elimination: Ordering of propositions; Loop detection
5 Coordination: Creating initial regression testing suite; Signature coordination; Summary progress report; Task assignment for next week

Grammar

All projects will use the same grammar and precedence rules. As the course proceeds, we will enlarge this grammar.

Whitespace
  space ( ) tab (\t) newline (\n) form feed (\f)
  other characters not listed below are illegal

Comment
  % to newline (\n)
  all characters except newline (\n) are allowed in comment

Atomic Proposition
  P  identifiers starting with letter A-Z or a-z
     followed by letters A-Z or a-z or digits 0-9
     identifiers are case-sensitive

Proposition
  A ::= P
      | ~ A         % negation
      | A & A       % conjunction
      | A v A       % disjunction
      | A => A      % implication
      | T           % truth
      | F           % falsehood
      | (A)         % parentheses to override precedence
  Operator Precedence  ~ > & > v > =>
  & v are left associative
  => is right associative

Declaration
  D ::= prove A.    % prove A
      | refute A.   % refute A

File Contents
  F ::=             % empty
      | D F         % declaration

Note that disjunction (v) may require surrounding whitespace for a correct parse since it is represent by a letter.

Reading

Handout 12 on Forward Sequent Calculus (also availabe in PDF format).