It is proved that the free product state, in the reduced free product of C–algebras, is faithful if the states one started with are faithful. The reduced free product of C–algebras was introduced by Voiculescu as the appropriate construction for C–algebras in the setting of his theory of freeness [1]. (See also the book [2]). Given a set I and for each ι ∈ I a unital C–algebra Aι with a state φ...

We investigate the conditions under which quasianalysis, i.e., Carnap’s method of abstraction in his Aufbau, yields adequate results. In particular, we state both necessary and sufficient conditions for the socalled faithfulness and fullness of quasianalysis, and analyze adequacy as the conjunction of faithfulness and fullness. It is shown that there is no method of (re-)constructing properties...

Phonological processes and structures are often limited to a particular set of a language’s words, such as loanwords, Latinate words in English, or Yamato words in Japanese. Typically, the etymologically older, or “core” set of words is more restricted in the structures that it permits, and is (hence) subject to more processes. To capture such restrictions in Optimality Theory, Itô and Mester (...

The paper discusses phonologically motivated gaps in inflectional paradigms and builds further on the analysis in Rice (2005). In that paper, we see an approach to modeling gaps based on a tension between markedness constraints, faithfulness constraints, and constraints which require the expression of morphological categories. Here we explore the prediction that constraints requiring the expres...

Using the flexibility of recently developed methods for causal discovery based on Boolean satisfiability (SAT) solvers, we encode a variety of assumptions that weaken the Faithfulness assumption. The encoding results in a number of SAT-based algorithms whose asymptotic correctness relies on weaker conditions than are standardly assumed. This implementation of a whole set of assumptions in the s...

I prove that there are phonological patterns which are expressible by ordered rewrite rules but not by any Optimality Theoretic (OT) grammar whose constraint set contains only markedness constraints and single–state faithfulness constraints, i.e. faithfulness constraints that assign violation marks to pairs of single input–output segments in correspondence, with no reference to other segments i...

In this paper we show how Jessen & Ringen’s (2002) analysis of voicing in German stops can be extended to account for the voicing of German fricatives. It is argued that while stops in German contrast for the feature [spread glottis], fricatives contrast for [voice] (and [spread glottis]). Our analysis, which involves presonorant faithfulness, is compared to an analysis with coda devoicing. We ...