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Incremental Dynamics
, 1998
"... An incremental semantics for a logic with dynamic binding is developed on the basis of a variable free notation for dynamic logic. The variable free indexing mechanism guarantees that active registers are never overwritten by new quantifier actions. The resulting system has the same expressive power ..."
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Cited by 17 (4 self)
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An incremental semantics for a logic with dynamic binding is developed on the basis of a variable free notation for dynamic logic. The variable free indexing mechanism guarantees that active registers are never overwritten by new quantifier actions. The resulting system has the same expressive power as Dynamic Predicate Logic or Discourse Representation Theory, but comes with a more well behaved consequence relation. A calculus for dynamic reasoning with anaphora is presented and its soundness and completeness are established. Incremental dynamic logic provides an explicit account of anaphoric context and yields new insight into the dynamics of anaphoric linking in reasoning. 1991 Mathematics Subject Classification: 03B65, 68Q55 1991 Computing Reviews Classification System: F.3.1, F.3.2, I.2.4, I.2.7 Keywords and Phrases: dynamic semantics of natural language, complete calculus for dynamic reasoning with anaphora, incremental interpretation, monotonic semantics, anaphora and context ...
Contexts in Dynamic Predicate Logic
 JOURNAL OF LANGUAGE, LOGIC AND INFORMATION
, 1998
"... In this paper we introduce a notion of context for Groenendijk & Stokhof's Dynamic Predicate Logic DPL. We use these contexts to give acharacterization of the relations on assignments that can be generated by composition from tests/conditions and random resettings in the case that we areworking over ..."
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Cited by 14 (1 self)
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In this paper we introduce a notion of context for Groenendijk & Stokhof's Dynamic Predicate Logic DPL. We use these contexts to give acharacterization of the relations on assignments that can be generated by composition from tests/conditions and random resettings in the case that we areworking over an infinite domain. These relations are precisely the ones definable in DPL if we allow ourselves arbitrary tests as a starting point. We discuss some possible extensions of DPL and the way these extensions interact with our notion of context.
Dynamic Reasoning Without Variables
, 1997
"... A variable free notation for dynamic logic is proposed which takes its cue from De Bruijn's variable free notation for lambda calculus. De Bruijn indexing replaces variables by indices which indicate the distance to their binders. We propose to use reverse De Bruijn indexing, which works almost the ..."
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Cited by 1 (1 self)
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A variable free notation for dynamic logic is proposed which takes its cue from De Bruijn's variable free notation for lambda calculus. De Bruijn indexing replaces variables by indices which indicate the distance to their binders. We propose to use reverse De Bruijn indexing, which works almost the same, only now the indices refer to the depth of the binding operator in the formula. The resulting system is analysed at length and applied to a new rational reconstruction of discourse representation theory. It is argued that the present system of dynamic logic without variables provides an explicit account of anaphoric context and yields new insight into the dynamics of anaphoric linking in reasoning. A calculus for dynamic reasoning with anaphora is presented and its soundness and completeness are established. 1991 Mathematics Subject Classification: 03B65, 68Q55, 1991 Computing Reviews Classification System: I.2.4, I.2.7 Keywords and Phrases: dynamic semantics, natural language proce...