A feasible theory of truth over combinatory algebra

We define an applicative theory of truth TPT which proves totality exactly for the polynomial time computable functions. TPT has natural and simple axioms since nearly all its truth axioms are standard for truth theories over an applicative framework. The only exception is the axiom dealing with the word predicate. The truth predicate can only reflect elementhood in the words for terms that have smaller length than a given word. This makes it possible to achieve the very low proof-theoretic strength. Truth induction can be allowed without any constraints. For these reasons the system TPT has the high expressive power one expects from truth theories. It allows embeddings of feasible systems of explicit mathematics and bounded arithmetic. The proof that the theory TPT is feasible is not easy. It is not possible to apply a standard realisation approach. For this reason we develop a new realisation approach whose realisation functions work on directed acyclic graphs. In this way, we can express and manipulate realisation information more efficiently.

Nominalization and nominalization-based constructions in Galo

This paper describes nominalization and nominalization-based constructions in Galo, a Tibeto-Burman language of the Tani branch spoken in North East India. Nominalizers in Galo are divided into primary and secondary sets, while nominalization-based constructions are divided into two types: nominalized clauses and clausal nominalizations. Both primary and secondary nominalizers help form nominalized clauses, which are uninflected, exhibit a genitive subject, and enter into nominal complement and relative clause constructions. Clausal nominalizations are formed by primary nominalizers only, may be inflected, exhibit a nominative subject, and in general take on a more main clause-like structure and set of functions. Following this basic description, the diachronic origins of Galo nominalizers are discussed, and the Galo forms and patterns are situated in terms of a broader typology of nominalization in Tibeto-Burman.

Referential hierarchies: A new look at some historical and typological patterns

This paper proposes a diachronic typology for the various patterns that have been referred to as Hierarchical Alignment or Inverse Alignment. Previous typological studies have tried to explain such patterns as grammatical reflections of a universal Referential Hierarchy, in which first person outranks second person outranks third person and humans outrank other animates outrank inanimates. However, our study shows that most of the formal properties of hierarchy-sensitive constructions are essentially predictable from their historical sources. We have identified three sources for hierarchical person marking, three for direction marking, two for obviative case marking, and one for hierarchical constituent ordering. These sources suggest that there is more than one explanation for hierarchical alignment: one is consistent with Givón’s claim that hierarchical patterns are a grammaticalization of generic topicality; another is consistent with DeLancey’s claim that hierarchies reflect the deictic distinction between present (1/2) and distant (3) participants; another is simply a new manifestation of a common asymmetrical pattern, the use of zero marking for third persons. More importantly, the evolution of hierarchical grammatical patterns does not reflect a consistent universal ranking of participants – at least in those cases where we can see (or infer) historical stages in the evolution of these properties, different historical stages appear to reflect different hierarchical rankings of participants, especially first and second person. This leads us to conclude that the diversity of hierarchical patterns is an artifact of grammatical change, and that in general, the presence of hierarchical patterns in synchronic grammars is not somehow conditioned by some more general universal hierarchy.