Syntactic Computation as Labelled Deduction: WH a case study

This paper addresses the question "Why do WH phenomena occur with the particular cluster of properties observed across languages -- long-distance dependencies, WH-in situ, partial movement constructions, reconstruction, crossover etc." These phenomena have been analysed by invoking a number of discrete principles and categories, but have so far resisted a unified treatment. The explanation proposed is set within a model of natural language understanding in context, where the task of understanding is taken to be the incremental building of a structure over which the semantic content is defined. The formal model is a composite of a labelled type-deduction system, a modal tree logic, and a set of rules for describing the process of interpreting the string as a set of transition states. A dynamic concept of syntax results, in which in addition to an output structure associated with each string (analogous to the level of LF), there is in addition an explicit meta-level description of the process whereby this incremental process takes place. This paper argues that WH-related phenomena can be unified by adopting this dynamic perspective. The main focus of the paper is on WH-initial structures, WH in situ structures, partial movement phenomena, and crossover phenomena. In each case, an analysis is proposed which emerges from the general characterisatioan of WH structures without construction-specific stipulation.Articl

The partition semantics of questions, syntactically

Groenendijk and Stokhof (1984, 1996; Groenendijk 1999) provide a logically attractive theory of the semantics of natural language questions, commonly referred to as the partition theory. Two central notions in this theory are entailment between questions and answerhood. For example, the question "Who is going to the party?" entails the question "Is John going to the party?", and "John is going to the party" counts as an answer to both. Groenendijk and Stokhof define these two notions in terms of partitions of a set of possible worlds. We provide a syntactic characterization of entailment between questions and answerhood . We show that answers are, in some sense, exactly those formulas that are built up from instances of the question. This result lets us compare the partition theory with other approaches to interrogation -- both linguistic analyses, such as Hamblin's and Karttunen's semantics, and computational systems, such as Prolog. Our comparison separates a notion of answerhood into three aspects: equivalence (when two questions or answers are interchangeable), atomic answers (what instances of a question count as answers), and compound answers (how answers compose).Comment: 14 page

Boolean Dependence Logic and Partially-Ordered Connectives

We introduce a new variant of dependence logic called Boolean dependence logic. In Boolean dependence logic dependence atoms are of the type =(x_1,...,x_n,\alpha), where \alpha is a Boolean variable. Intuitively, with Boolean dependence atoms one can express quantification of relations, while standard dependence atoms express quantification over functions. We compare the expressive power of Boolean dependence logic to dependence logic and first-order logic enriched by partially-ordered connectives. We show that the expressive power of Boolean dependence logic and dependence logic coincide. We define natural syntactic fragments of Boolean dependence logic and show that they coincide with the corresponding fragments of first-order logic enriched by partially-ordered connectives with respect to expressive power. We then show that the fragments form a strict hierarchy.Comment: 41 page

A Team Based Variant of CTL

We introduce two variants of computation tree logic CTL based on team semantics: an asynchronous one and a synchronous one. For both variants we investigate the computational complexity of the satisfiability as well as the model checking problem. The satisfiability problem is shown to be EXPTIME-complete. Here it does not matter which of the two semantics are considered. For model checking we prove a PSPACE-completeness for the synchronous case, and show P-completeness for the asynchronous case. Furthermore we prove several interesting fundamental properties of both semantics.Comment: TIME 2015 conference version, modified title and motiviatio

Reviving the parameter revolution in semantics

Montague and Kaplan began a revolution in semantics, which promised to explain how a univocal expression could make distinct truth-conditional contributions in its various occurrences. The idea was to treat context as a parameter at which a sentence is semantically evaluated. But the revolution has stalled. One salient problem comes from recurring demonstratives: "He is tall and he is not tall". For the sentence to be true at a context, each occurrence of the demonstrative must make a different truth-conditional contribution. But this difference cannot be accounted for by standard parameter sensitivity. Semanticists, consoled by the thought that this ambiguity would ultimately be needed anyhow to explain anaphora, have been too content to posit massive ambiguities in demonstrative pronouns. This article aims to revived the parameter revolution by showing how to treat demonstrative pronouns as univocal while providing an account of anaphora that doesn't end up re-introducing the ambiguity

Parameterised Complexity of Propositional Inclusion and Independence Logic

In this work we analyse the parameterised complexity of propositional inclusion (PINC) and independence logic (PIND). The problems of interest are model checking (MC) and satisfiability (SAT). The complexity of these problems is well understood in the classical (non-parameterised) setting. Mahmood and Meier (FoIKS 2020) recently studied the parameterised complexity of propositional dependence logic (PDL). As a continuation of their work, we classify inclusion and independence logic and thereby come closer to completing the picture with respect to the parametrised complexity for the three most studied logics in the propositional team semantics setting. We present results for each problem with respect to 8 different parameterisations. It turns out that for a team-based logic L such that L-atoms can be evaluated in polynomial time, then MC parameterised by teamsize is FPT. As a corollary, we get an FPT membership under the following parameterisations: formula-size, formula-depth, treewidth, and number of variables. The parameter teamsize shows interesting behavior for SAT. For PINC, the parameter teamsize is not meaningful, whereas for PDL and PIND the satisfiability is paraNP-complete. Finally, we prove that when parameterised by arity, both MC and SAT are paraNP-complete for each of the considered logics.Comment: A revised versio