11.2.3 Syntax of DRSs and DRS-Conditions

The formal, recursive definition of DRSs and DRS-Conditions.

  1. If are discourse referents () and () are DRS-conditions then the following is a DRS:

  2. If is a relation symbol of arity ( ), and are some discourse referents, then is a DRS-Condition;

  3. If and are first-order terms, then is a DRS-Condition;

  4. If and are DRSs, then and are DRS-Conditions;

  5. If is a DRS, then is a DRS-Condition;

  6. Nothing is a DRS or DRS-Condition unless it can be shown to be so using clauses 1-5.

Here, first-order terms (clause 3) denote either discourse referents or constants. We sometimes refer to DRS-Conditions of the form licensed by clauses 2-3 as ``basic'' conditions, while those licensed by clauses 3-5 are called complex conditions. Note that, in a way, DRSs bear a lot of similarities with the first-order logic formula syntax. As in first-order logic, we have the boolean connectors (, , ) to create nested boxes and express implication, disjunction, and negation. But unlike first-order logic, we don't have explicit conjunction, and we don't have explicit quantifiers. With a formal definition of the syntax of DRSs at our disposal, we are now in a good position to define subordination (a relation between DRSs), which then opens the way to define accessibility.

Aljoscha Burchardt, Stephan Walter, Alexander Koller, Michael Kohlhase, Patrick Blackburn and Johan Bos
Version 1.2.5 (20030212)