## Discourse Representation Structure

Discourse Representation Structures (DRSs) can be displayed in different formats. In the PMB we use two different formats: the box format, used for visualisation purposes; and the clause format, used for evaluation purposes.

Discourse Representation Structures (box notation)

There are basic and complex DRS-conditions. Terms are either variables or constants. Basic DRS-conditions are defined as follows:

• If SYM is a non-logical symbol, SNS a sense, and x is a term then SYM.SNS(x) is a basic DRS-condition (wordnet concepts);
• If ROL is a symbol denoting a VerbNet role and x and y are terms then ROL(x,y) is a basic DRS-condition (thematic roles);
• If x and y are terms then x=y, x≠y, x≈y, x<y, x>y, x≤y, x≥y, x≺y, x≻y, x⋈y are basic DRS-conditions (comparison operators).
The complex DRS-conditions are defined as follows:
• If B is a DRS, then ¬B, ◇B, and □B are complex DRS-conditions (negation and modals);
• If x is a variable, and B is a DRS, then x:B is a complex condition (propositional);
• If B and B' are DRSs, then B⇒B' and B∨B' are complex conditions (implication and disjunction).
A DRS is defined as follows:
• If D is a (possibly empty) set of discourse referents, and C a (possibly empty) set of DRS-conditions, then <D,C> is a (basic) DRS;
• If B is a (basic) DRS, and B' a DRS, then B↓B' is a (segmented) DRS;
• If U is a set of DRSs, and R a set of discourse relations, then <U,R> is a (segmented) DRS.

Discourse Representation Structures (SBN)

SBN (sequence box notation) is a way to represent DRS without using variables. The variables are replaced by indices that refer backwards or forwards in a sequence of concepts. SBN is defined as a sequence of concepts, roles (with 0-drop, that means the first argument of a role is always the previous concept), and discourse relations. In the PMB, DRSs in SBN are aligned with the input text, but these alignment is not always perfect and not part of the meaning representation proper.

Discourse Representation Structures (clause notation)

A DRS in clause notation is an unordered set of clauses that describe a DRS. The first argument of a clause is always a variable for a DRS. The second argument determines the type of the clause. The third and fourth argument are always variables or constants (constants are enclosed in double quotes). The following clauses are permitted:

Clause TypeExplanation
B REF XDRS B has discourse referent X
B NOT B'DRS B contains DRS-condition ¬ B' (it is not the case that)
B POS B'DRS B contains DRS-condition ◇ B' (it is possible that)
B NEC B'DRS B contains DRS-condition □ B' (it is necessary that)
B IMP B' B''DRS B contains DRS-condition B' ⇒ B'' (conditional)
B DIS B' B''DRS B contains DRS-condition B' ∨ B'' (disjunction)
B PRP X B'DRS B contains DRS-condition X : B' (propositional)
B SYM SNS XDRS B contains one-place predicate SYM with sense SNS applied to X
B ROL X YDRS B contains role ROL that holds between X and Y
B REL B' B''(segmented) DRS B contains discourse relation REL that holds between DRSs B' and B''
B DRS B'(segmented) DRS B has DRS B'
B EQU X YDRS B contains DRS-condition X = Y
B NEQ X YDRS B contains DRS-condition X ≠ Y (not equal to)
B APX X YDRS B contains DRS-condition X ≈ Y (approximately equal to)
B LES X YDRS B contains DRS-condition X < Y (less than)
B LEQ X YDRS B contains DRS-condition X ≤ Y (less or equal than)
B TPR X YDRS B contains DRS-condition X ≺ Y (temporally precedes; before)
B TSU X YDRS B contains DRS-condition X ≻ Y (temporally succeeds; after)
B TIN X YDRS B contains DRS-condition X ⊏ Y (temporally includes)
B TCT X YDRS B contains DRS-condition X ⊐ Y (temporally contains)
B TAB X YDRS B contains DRS-condition X ⋈ Y (temporally abuts; meets)
B SZP X YDRS B contains DRS-condition X ∕ Y (spatial above)
B SZN X YDRS B contains DRS-condition X ∖ Y (spatial under)
B SXP X YDRS B contains DRS-condition X » Y (spatial behind)
B SXN X YDRS B contains DRS-condition X « Y (spatial before)
B STI X YDRS B contains DRS-condition X ⨃ Y (spatial topological inside)
B STO X YDRS B contains DRS-condition X ᑘ Y (spatial topological outside)
B SY1 X YDRS B contains DRS-condition X ∥ Y (spatial beside)
B SY2 X YDRS B contains DRS-condition X ⚮ Y (spatial between)
B SXY X YDRS B contains DRS-condition X ≖ Y (spatial around)

The semantic matching tools expects DRSs in clause format with the following technical conventions. They are stored in a simple text file encoded in UTF-8. Each line contains one clause, and clause arguments are separated by one or more spaces or tabs. Comments can be added using a percentage symbol. Any information after this sign is considered to be not part of the clauses. A file can contain more than one DRS, in which case individual DRSs are separated by an empty line (not containing a comment).