A New Arithmetically Incomplete First- Order Extension of Gl All Theorems of Which Have Cut Free Proofs

Reference [12] introduced a novel formula to formula translation tool (“formulators”) that enables syntactic metatheoretical investigations of first-order modal logics, bypassing a need to convert them first into Gentzen style logics in order to rely on cut elimination and the subformula property. In fact, the formulator tool, as was already demonstrated in loc. cit., is applicable even to the metatheoretical study of logics such as QGL, where cut elimination is (provably, [2]) unavailable. This paper applies the formulator approach to show the independence of the axiom schema _A ! _8xA of the logics M3 and ML3 of [17, 18, 11, 13]. This leads to the conclusion that the two logics obtained by removing this axiom are incomplete, both with respect to their natural Kripke structures and to arithmetical interpretations. In particular, the so modified ML3 is, similarly to QGL, an arithmetically incomplete first-order extension of GL, but, unlike QGL, all its theorems have cut free proofs. We also establish here, via formulators, a stronger version of the disjunction property for GL and QGL without going through Gentzen versions of these logics (compare with the more complex proofs in [2, 8]).This research was partially supported by NSERC grant No. 8250

The Living Psalms

Reviewed Book: Westermann, Claus. The Living Psalms. Grand Rapids: Eerdmans; Edinburgh: T & T Clark, 1989

From Jewish Prophet to Gentile God: The Origins and Development of New Testament Christology

Reviewed Book: Casey, Maurice. from Jewish Prophet to Gentile God: The Origins and Development of New Testament Christology. Cambridge: James Clarke; Louisville, Ky: Westminster/John Knox Press, 1991. Edward Cadbury lectures; 1985-1986

Method and system for diagnostics of apparatus

Proposed is a method, implemented in software, for estimating fault state of an apparatus outfitted with sensors. At each execution period the method processes sensor data from the apparatus to obtain a set of parity parameters, which are further used for estimating fault state. The estimation method formulates a convex optimization problem for each fault hypothesis and employs a convex solver to compute fault parameter estimates and fault likelihoods for each fault hypothesis. The highest likelihoods and corresponding parameter estimates are transmitted to a display device or an automated decision and control system. The obtained accurate estimate of fault state can be used to improve safety, performance, or maintenance processes for the apparatus

Bilingual Complex Abstract Lexical Structure and Its Relevance to Interlanguage Studies

This study adopts two assumptions about abstract lexical structure. One is that lexical structure is modular: lexical information is organized into subsystems pointing to different levels of linguistic structure, and parts of lexical structure can be split and recombined. The other concerns the sources of morphemes actually occurring in surface strings. As commonly recognized, abstract lexical structure contains three levels: lexical-conceptual structure, predicate-argument structure, and morphological realization patterns. This study argues that abstract lexical structure becomes “complex” because the bilingual mental lexicon contains lemmas (i.e., abstract entries about lexemes) from different sources, such as learners’ first language, their target language, and their interlanguage. By adopting a multi-layered speech production model (Levelt, 1989; Myers-Scotton & Jake, 2001; Wei, 2002, 2015, 2020), it further argues that different types of morphemes are accessed at different levels of language production, resulting in different degrees of learning difficulty (an implicational hierarchy of second language morpheme acquisition) and different types of learner errors in interlanguage production. The typical instances of learner errors for the study are collected from interlanguage performance by adult second language learners with various first language backgrounds. This study aims to explore the nature of the bilingual mental lexicon and mechanisms of interlanguage development

Paraphrases and summaries: A means of clarification or a vehicle for articulating a preferred version of student accounts?

The use of group discussions as a means to facilitate learning from experiences is well documented in adventure education literature. Priest and Naismith (1993) assert that the use of the circular discussion method, where the leader poses questions to the participants, is the most common form of facilitation in adventure education. This paper draws on transcripts of facilitation sessions to argue that the widely advocated practice of leader summaries or paraphrases of student responses in these sessions functions as a potential mechanism to control and sponsor particular knowledge(s). Using transcripts from recorded facilitation sessions the analysis focuses on how the leader paraphrases the students’ responses and how these paraphrases or ‘formulations’ function to modify or exclude particular aspects of the students’ responses. I assert that paraphrasing is not simply a neutral activity that merely functions to clarify a student response, it is a subtle means by which the leader of the session can, often inadvertently or unknowingly, alter the student’s reply with the consequence of favouring particular knowledge(s). Revealing the subtle work that leader paraphrases perform is of importance for educators who claim to provide genuine opportunities for students to learn from their experience