Complex copula systems as suppletive alomorphy

Languages are known to vary in the number of verbs they exhibit corresponding to English "be", in the distribution of such copular verbs, and in the presence or absence of a distinct verb for possession sentences corresponding to English "have". This paper offers novel arguments for the position that such differences should be modeled in terms of suppletive allomorphy of the same syntactic element (here dubbed v BE), employing a Late Insertion- based framework. It is shown that such a suppletive allomorphy approach to complex copula systems makes three predictions that distinguish it from non-suppletion-based alternatives (concerning decomposition, possible and impossible syncretisms, and Impoverishment), and that these predictions seem to be correct (although a full test of the possible and impossible syncretisms prediction is not possible in the current state of knowledge)

Parallel grammaticalizations in Tibeto-Burman : evidence of Sapir's 'Drift'

In chapters seven and eight of his book Language, Sapir talked about what he called ‘drift’, the changes that a language undergoes through time [...]. Dialects of a language are formed when that language is broken into different segments that no longer move along the same exact drift. Even so, the general drift of a language has its deep and its shallow currents; those features that distinguish closely related dialects will be of the rapid, shallow currents, while the deeper, slower currents may remain consistent between the dialects for millennia. It is this latter type that Sapir felt is ‘fundamental to the genius of the language’ (p. 172), and he said that ‘The momentum of the more fundamental, the pre-dialectal, drift is often such that languages long disconnected will pass through the same or strikingly similar phases’ (p. 172)

Resource-Bound Quantification for Graph Transformation

Graph transformation has been used to model concurrent systems in software engineering, as well as in biochemistry and life sciences. The application of a transformation rule can be characterised algebraically as construction of a double-pushout (DPO) diagram in the category of graphs. We show how intuitionistic linear logic can be extended with resource-bound quantification, allowing for an implicit handling of the DPO conditions, and how resource logic can be used to reason about graph transformation systems

HoCHC: A Refutationally Complete and Semantically Invariant System of Higher-order Logic Modulo Theories

We present a simple resolution proof system for higher-order constrained Horn clauses (HoCHC) - a system of higher-order logic modulo theories - and prove its soundness and refutational completeness w.r.t. the standard semantics. As corollaries, we obtain the compactness theorem and semi-decidability of HoCHC for semi-decidable background theories, and we prove that HoCHC satisfies a canonical model property. Moreover a variant of the well-known translation from higher-order to 1st-order logic is shown to be sound and complete for HoCHC in standard semantics. We illustrate how to transfer decidability results for (fragments of) 1st-order logic modulo theories to our higher-order setting, using as example the Bernays-Schonfinkel-Ramsey fragment of HoCHC modulo a restricted form of Linear Integer Arithmetic

Classical Mathematics for a Constructive World

Interactive theorem provers based on dependent type theory have the flexibility to support both constructive and classical reasoning. Constructive reasoning is supported natively by dependent type theory and classical reasoning is typically supported by adding additional non-constructive axioms. However, there is another perspective that views constructive logic as an extension of classical logic. This paper will illustrate how classical reasoning can be supported in a practical manner inside dependent type theory without additional axioms. We will see several examples of how classical results can be applied to constructive mathematics. Finally, we will see how to extend this perspective from logic to mathematics by representing classical function spaces using a weak value monad.Comment: v2: Final copy for publicatio