On the Correspondence between Display Postulates and Deep Inference in Nested Sequent Calculi for Tense Logics

We consider two styles of proof calculi for a family of tense logics, presented in a formalism based on nested sequents. A nested sequent can be seen as a tree of traditional single-sided sequents. Our first style of calculi is what we call "shallow calculi", where inference rules are only applied at the root node in a nested sequent. Our shallow calculi are extensions of Kashima's calculus for tense logic and share an essential characteristic with display calculi, namely, the presence of structural rules called "display postulates". Shallow calculi enjoy a simple cut elimination procedure, but are unsuitable for proof search due to the presence of display postulates and other structural rules. The second style of calculi uses deep-inference, whereby inference rules can be applied at any node in a nested sequent. We show that, for a range of extensions of tense logic, the two styles of calculi are equivalent, and there is a natural proof theoretic correspondence between display postulates and deep inference. The deep inference calculi enjoy the subformula property and have no display postulates or other structural rules, making them a better framework for proof search

Pottsian LFG

Potts (2005) provides an elegant and influential approach to the syntax and semantics of a wide range of 'parenthetical' constructions, including various kinds of supplementals/appositives and expressives, which have not received much attention in the LFG literature. The prospect of wholesale importation of Pottsian analyses for such constructions is appealing. However, there are (as Potts himself notes) problems with his approach from a resource sensitive perspective, such as is often assumed in LFG approaches to the syntax semantics interface. Potts sketches, but does not develop, a way of overcoming these problems. In this paper we attempt to develop his proposal and explore ways in which it can be implemented in the architecture of LFG. For exemplification, we focus on supplemental ('appositive', non-restrictive) relative clauses in English. A side effect of our discussion is thus a proposal for an LFG analysis of this construction, which appears to have been neglected hitherto

Structural Interactions and Absorption of Structural Rules in BI Sequent Calculus

Development of a contraction-free BI sequent calculus, be it in the sense of G3i or G4i, has not been successful in literature. We address the open problem by presenting such a sequent system. In fact our calculus involves no structural rules

Resource Splitting and Reintegration with Supplementals

In this paper we survey the various ways of expressing modality in Urdu/Hindi and show that Urdu/Hindi modals provide interesting insights on current discussions of the semantics of modality. There are very few dedicated modals in Urdu/Hindi: most of which has been arrived at constructionally via a combination of a certain kind of verb with a certain kind of embedded verb form and a certain kind of case. Among the range of constructions yielded by such combinations, there is evidence for a two-place modal operator in addition to the one-place operator usually assumed in the literature. We also discuss instances of the Actuality Entailment, which had been shown to be sensitive to aspect, but in Urdu/Hindi appears to be sensitive to aspect only some of the time, depending on the type of modal verb. Indeed, following recent proposals by Ramchand (2011), we end up with a purely lexical account of modality and the Actuality Entailment, rather than the structural one put forward by Hacquard (2010)

External Validity: From Do-Calculus to Transportability Across Populations

The generalizability of empirical findings to new environments, settings or populations, often called "external validity," is essential in most scientific explorations. This paper treats a particular problem of generalizability, called "transportability," defined as a license to transfer causal effects learned in experimental studies to a new population, in which only observational studies can be conducted. We introduce a formal representation called "selection diagrams" for expressing knowledge about differences and commonalities between populations of interest and, using this representation, we reduce questions of transportability to symbolic derivations in the do-calculus. This reduction yields graph-based procedures for deciding, prior to observing any data, whether causal effects in the target population can be inferred from experimental findings in the study population. When the answer is affirmative, the procedures identify what experimental and observational findings need be obtained from the two populations, and how they can be combined to ensure bias-free transport.Comment: Published in at http://dx.doi.org/10.1214/14-STS486 the Statistical Science (http://www.imstat.org/sts/) by the Institute of Mathematical Statistics (http://www.imstat.org). arXiv admin note: text overlap with arXiv:1312.748