Beta reduction constraints

The constraint language for lambda structures (CLLS) can model lambda terms that are known only partially. In this paper, we introduce beta reduction constraints to describe beta reduction steps between partially known lambda terms. We show that beta reduction constraints can be expressed in an extension of CLLS by group parallelism. We then extend a known semi-decision procedure for CLLS to also deal with group parallelism and thus with beta-reduction constraints

Underspecified beta reduction

For ambiguous sentences, traditional semantics construction produces large numbers of higher-order formulas,which must then be beta-reduced individually. Underspecified versions can produce compact descriptions of all readings, but it is not known how to perform beta reduction on these descriptions. We show how to do this using beta reduction constraints in the constraint language for lambda-structures (CLLS)

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

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

Beta reduction constraints

www.ps.uni-sb.de/~{bodirsky,erk,koller,niehren} Abstract. The constraint language for lambda structures (CLLS) can model lambda terms that are known only partially. In this paper, we introduce beta reduction constraints to describe beta reduction steps between partially known lambda terms. We show that beta reduction constraints can be expressed in an extension of CLLS by group parallelism. We then extend a known semi-decision procedure for CLLS to also deal with group parallelism and thus with beta-reduction constraints.