Soames on Russell’s logic: a reply

In “What is History For?,” Scott Soames responds to criticisms of his treatment of Russell’s logic in volume 1 of his Philosophical Analysis in the Twentieth Century. This note rebuts two of Soames’s replies, showing that a first-order presentation of Russell’s logic does not fit the argument of the Introduction to Mathematical Philosophy, and that Soames’s contextual definition of classes does not match Russell’s contextual definition of classes. In consequence, Soames’s presentation of Russell’s logic misrepresents what Russell took to be its technical achievement and its philosophical significance.     

Arguments by Parallels in the Epistemological Works of Phya pa Chos kyi seng ge

The works of the Tibetan logician Phya pa Chos kyi seng ge (1109–1169) make abundant use of a particular type of argument that I term ‘argument by parallels’. Their main characteristic is that the instigator of the argument, addressing a thesis in a domain A, introduces a parallel thesis in an unrelated domain B. And in the ensuing dialogue, each of the instigator’s statements consists in replicating his interlocutor’s previous assertion, mutatis mutandis, in the other domain (A or B). I show that such a dialogue involves two parallel arguments that develop in an intersecting zigzag pattern, and discuss the principles involved in the establishment of the conclusion from the perspective of parity of reasoning and analogical argument. I examine the overall rhetorical strategy directing the use of arguments by parallels and the pedagogical and explanatory functions they can serve. I also evaluate the plausibility of their use in Phya pa Chos kyi seng ge’s works mirroring a contemporary practice of oral debate, and reflect on the status of such arguments in the framework of Indo-Tibetan logic.

儒家智者的逻辑——析荀子正名论

荀子适应当时社会需要 ,从儒家智者的视角 ,创发孔子正名的逻辑内涵 ,建构以概念论为中心的逻辑体系 ,继墨辩之后把中国古代逻辑推向又一高峰。荀子对概念论和语言论、本体论、认识论、判断论、推理论、诡辩论、语言规范化、华夏大一统的相关论述 ,是当前仍有积极价值的学术精华。以现代方法揭示荀子正名论的逻辑意义 ,是中国逻辑元研究的课题。     

Logic programs, iterated function systems, and recurrent radial basis function networks

Graphs of the single-step operator for first-order logic programs—displayed in the real plane—exhibit self-similar structures known from topological dynamics, i.e., they appear to be fractals, or more precisely, attractors of iterated function systems. We show that this observation can be made mathematically precise. In particular, we give conditions which ensure that those graphs coincide with attractors of suitably chosen iterated function systems, and conditions which allow the approximation of such graphs by iterated function systems or by fractal interpolation. Since iterated function systems can easily be encoded using recurrent radial basis function networks, we eventually obtain connectionist systems which approximate logic programs in the presence of function symbols.     

Conflicting imperatives and dyadic deontic logic

Often a set of imperatives or norms seems satisfiable from the outset, but conflicts arise when ways to fulfill all are ruled out by unfortunate circumstances. Semantic methods to handle normative conflicts were devised by B. van Fraassen and J.F. Horty, but these are not sensitive to circumstances. The present paper extends these resolution mechanisms to circumstantial inputs, defines dyadic deontic operators accordingly, and provides a sound and (weakly) complete axiomatic system for such deontic semantics.     

Logic,Rules and Intention: The Principal Aim Argument

Stephen Mumford develops his view of sport spectatorship partly through a rejection of an argument he attributes to Best, which distinguishes between two categories of sports, the ‘purposive’ and the ‘aesthetic’, on the basis of the claim that they have different principal aims. This paper considers the principal aim argument and one feature of Mumford’s rejection of that argument, namely, Best’s observation that the distinctions to which he draws attention are based on logical differences. The paper argues that Mumford misconstrues Best’s argument by taking it to be about the intentions of players and athletes, while it is actually about a specific feature of the rules of each sport.     

A hierarchical state space approach to affective dynamics

Linear dynamical system theory is a broad theoretical framework that has been applied in various research areas such as engineering, econometrics and recently in psychology. It quantifies the relations between observed inputs and outputs that are connected through a set of latent state variables. State space models are used to investigate the dynamical properties of these latent quantities. These models are especially of interest in the study of emotion dynamics, with the system representing the evolving emotion components of an individual. However, for simultaneous modeling of individual and population differences, a hierarchical extension of the basic state space model is necessary. Therefore, we introduce a Bayesian hierarchical model with random effects for the system parameters. Further, we apply our model to data that were collected using the Oregon adolescent interaction task: 66 normal and 67 depressed adolescents engaged in a conflict-oriented interaction with their parents and second-to-second physiological and behavioral measures were obtained. System parameters in normal and depressed adolescents were compared, which led to interesting discussions in the light of findings in recent literature on the links between cardiovascular processes, emotion dynamics and depression. We illustrate that our approach is flexible and general: The model can be applied to any time series for multiple systems (where a system can represent any entity) and moreover, one is free to focus on various components of this versatile model.     

Innovations in computational type theory using Nuprl

For twenty years the Nuprl (“new pearl”) system has been used to develop software systems and formal theories of computational mathematics. It has also been used to explore and implement computational type theory (CTT)—a formal theory of computation closely related to Martin-Löf's intuitionistic type theory (ITT) and to the calculus of inductive constructions (CIC) implemented in the Coq prover.

This article focuses on the theory and practice underpinning our use of Nuprl for much of the last decade. We discuss innovative elements of type theory, including new type constructors such as unions and dependent intersections, our theory of classes, and our theory of event structures.

We also discuss the innovative architecture of Nuprl as a distributed system and as a transactional database of formal mathematics using the notion of abstract object identifiers. The database has led to an independent project called the Formal Digital Library, FDL, now used as a repository for Nuprl results as well as selected results from HOL, MetaPRL, and PVS. We discuss Howe's set theoretic semantics that is used to relate such disparate theories and systems as those represented by these provers.     

Model checking propositional dynamic logic with all extras

This paper presents a model checking algorithm for Propositional Dynamic Logic (PDL) with looping, repeat, test, intersection, converse, program complementation as well as context-free programs. The algorithm shows that the model checking problem for PDL remains PTIME-complete in the presence of all these operators, in contrast to the high increase in complexity that they cause for the satisfiability problem.     

Transfert de la conscience morphologique de l’arabe langue première au français langue seconde au cours des trois premières années d’apprentissage

There is a great deal of evidence to support the role of morphological awareness in reading development. However, towards second language acquisition, transfer of morphological awareness from first to second language (L1 to L2) is still discussed. The underlying question concerns the extent to which morphological awareness is a specific or universal process, and its dependence of linguistic features. The aim of this study is to examine cross-linguistic transfer of morphological awareness from Arabic L1 to French L2 (morphological awareness and word reading) at different level of learning French L2 (F_L2). 106 Tunisian children, whose first language is Arabic, in 1st (n = 29; mean age; 8; 10 years), 2nd (n = 33; mean age; 9; 9 years) or 3rd year (n = 44; mean age; 10; 10 years) of learning F_L2 participated to this study. Their morphological awareness (inflectional or derivational oddity detection tasks) and their performance in word reading (one minute test) were assessed in standard Arabic and French, as well as their vocabulary knowledge in French. A series of fixed-order hierarchical regression analysis was performed on derivational awareness performances, inflectional awareness performances and word reading performances in F_L2, controlling for effects of other important variables (e.g. French vocabulary, French morphological awareness with word reading scores as outcome variable and French inflectional or derivational awareness with French inflectional or derivational awareness scores as outcome variable respectively, Arabic word reading, etc.). Results show significant contributions of L1 morpho-derivational awareness on F_L2 morpho-derivational awareness in 2nd year (12%), and of L1 morphological awareness on reading words F_L2 in 3^rd year (5%). These results confirm the cross-linguistic transfer of morphological awareness, particularly derivational, from L1 to L2 among alphabetic — but orthographically and morphologically distances — languages. They also suggest that such a transfer could be relatively limited. It could appear during learning process after achieving a threshold in F_L2 and before specific L2 skills take place. Thus, beyond the morphological opacity of Arabic (nonlinear morphology) and linguistic distance between Arabic and French, the morphological transfer could appear on rich and important morphological dimension in L1 and suggest dealing with the nature of cross-linguistic abilities in depth.