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。     

Action negation and alternative reductions for dynamic deontic logics

Dynamic deontic logics reduce normative assertions about explicit complex actions to standard dynamic logic assertions about the relation between complex actions and violation conditions. We address two general, but related problems in this field. The first is to find a formalization of the notion of ‘action negation’ that (1) has an intuitive interpretation as an action forming combinator and (2) does not impose restrictions on the use of other relevant action combinators such as sequence and iteration, and (3) has a meaningful interpretation in the normative context. The second problem we address concerns the reduction from deontic assertions to dynamic logic assertions. Our first point is that we want this reduction to obey the free-choice semantics for norms. For ought-to-be deontic logics it is generally accepted that the free-choice semantics is counter-intuitive. But for dynamic deontic logics we actually consider it a viable, if not, the better alternative. Our second concern with the reduction is that we want it to be more liberal than the ones that were proposed before in the literature. For instance, Meyer's reduction does not leave room for action whose normative status is neither permitted nor forbidden. We test the logics we define in this paper against a set of minimal logic requirements.     

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.     

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.     

Contribution of upper trunk rotation to hand forward-backward movement and propulsion in front crawl strokes

The study aims to test three hypotheses: (a) the rotation of the upper trunk consists of roll, pitch and yaw of frequencies harmonic to the stroke frequency of the front crawl stroke, (b) the rotation of the upper trunk generates back-and-forth movements of the shoulders, which enhances the movements of the stroking arms, and (c) the angular velocities of roll, pitch and yaw are associated with hand propulsion (HP). Front crawl strokes performed by twenty male swimmers were measured with a motion capture system. The roll, pitch and yaw angles about the three orthogonal axes embedded in the upper trunk were determined as three sequential Cardan angles and their angular velocities were determined as the three respective components of the angular velocity. HP and the drag and lift components of HP (HP_D and HP_L) were estimated by the hand positions and the data from twelve pressure sensors attached on hands. The roll, pitch, and yaw angles were altered in frequencies harmonic to the stroke frequency during the front crawl stroke. Shoulders alternately moved back and forth due to the upper trunk rotation. In the pull phase the angular velocity of roll was correlated with HP_L (r = −0.62, p = 0.004). Based on the back-and-forth movements of the shoulders and roll motion relative to a hand movement, the arm-stroke technique of the front crawl swimming was discussed in terms of increasing the hand velocity and HP.     

Consciousness in a multilevel architecture: What causes the lateralization of effective connectivity under resting state?

Here we present our answers to a critical commentary by Elkhonon Goldberg on our recent publication (Velichkovsky et al., 2018). To avoid discussions about novelty effects in the human brain activity and memory processes, we narrowed down this response to a reanalysis of our data along the lines proposed in the commentary, namely to comparing the effective links between symmetrical brain structures during the first and the last parts of a prolonged resting-state fMRI experiment. We also tested for sex differences in our results and checked for a stability of top-down interactions during the course of experiment because learning is often expressed in the weakening of upper level control over low-level mechanisms. Our attempts to test the predictions based on the novelty hypothesis has led to mixed results suggesting that the discovered right-to-left dominance of causal connections at rest may have a deeper origin than supposed in the Goldberg’s commentary.     

Mimic automata: A novel formal model for mimic computing

In this paper, we aim to establish a mathematical model for mimic computing. To this end, we present a novel automaton called a mimic automaton. First, a one-dimensional cellular automaton is used for expressing some dynamic changes in the structure of a computing unit, a sequential automaton is employed to describe some state transitions, a hierarchical automaton is employed to express the different granularities of some computing units, and a probabilistic automaton is used to depict some random changes of a computing unit. Second, a mimic automaton is obtained by combining the various types of automata mentioned above in a certain logical relationship. Compared with the existing models of mimic computing, the new model portrays the operational semantics for a mimic computing system, and it can directly describe the behaviors of a system. Furthermore, the new model possesses a stronger generality.