Well-nested Context Unification

International audienceContext unification (CU) is the famous open problem of solving context equations for trees. We distinguish a new decidable fragment of CU - well-nested CU - and present a new unification algorithm that solves well-nested context equations in non-deterministic polynomial time. We show that minimal well-nested solutions of context equations can be composed from the material present in the equation. This surprising property is highly wishful when modeling natural language ellipsis in CU

Processing underspecified semantic representations in the constraint language for lambda structures

The constraint language for lambda structures (CLLS) is an expressive language of tree descriptions which combines dominance constraints with powerful parallelism and binding constraints. CLLS was introduced as a uniform framework for defining underspecified semantics representations of natural language sentences, covering scope, ellipsis, and anaphora. This article presents saturation-based algorithms for processing the complete language of CLLS. It also gives an overview of previous results on questions of processing and complexity.Liegt nicht vor

Well-nested Context Unification

International audienceContext unification (CU) is the famous open problem of solving context equations for trees. We distinguish a new decidable fragment of CU - well-nested CU - and present a new unification algorithm that solves well-nested context equations in non-deterministic polynomial time. We show that minimal well-nested solutions of context equations can be composed from the material present in the equation. This surprising property is highly wishful when modeling natural language ellipsis in CU

Parallelism and tree regular constraints

Parallelism constraints are logical descriptions of trees. Parallelism constraints subsume dominance constraints and are equal in expressive power to context unification. Parallelism constraints belong to the constraint language for lambda structures (CLLS) which serves for modeling natural language semantics. In this paper, we investigate the extension of parallelism constraints by tree regular constraints. This canonical extension is subsumed by the monadic second-order logic over parallelism constraints. We analyze the precise expressiveness of this extension on basis of a new relationship between tree automata and logic. Our result is relevant for classifying different extensions of parallelism constraints, as in CLLS. Finally, we prove that parallelism constraints and context unification remain equivalent when extended with tree regular constraints

Processing underspecified semantic representations in the constraint language for lambda structures

The constraint language for lambda structures (CLLS) is an expressive language of tree descriptions which combines dominance constraints with powerful parallelism and binding constraints. CLLS was introduced as a uniform framework for defining underspecified semantics representations of natural language sentences, covering scope, ellipsis, and anaphora. This article presents saturation-based algorithms for processing the complete language of CLLS. It also gives an overview of previous results on questions of processing and complexity.Liegt nicht vor