SOSA'S MOORE AND THE NEW DOGMATISTS

Abstract: Some seventy years ago, G. E. Moore invoked his own sensory experience (as of a hand before him in the right circumstances), added some philosophical analysis about externality, and took himself to have offered his "Proof" of the existence of an external world. Current neo-Mooreans either reject completely the standard negative assessment of the Proof or qualify it substantially. For Sosa, the Proof can be persuasive, but only when read literally as offering reasons for the conclusion that there is at least one external object—rather than that the prover is justified in believing, or even knowing, that there is at least one external object. Sosa, then, is a neo-Moorean—though not of the sort we might expect in light of the ongoing debate about the Proof. I argue that Sosa needs to say more about the circularity often thought to vitiate the Proof before we can accept his view.     

Computer supported mathematics with Ωmega

Classical automated theorem proving of today is based on ingenious search techniques to find a proof for a given theorem in very large search spaces—often in the range of several billion clauses. But in spite of many successful attempts to prove even open mathematical problems automatically, their use in everyday mathematical practice is still limited.The shift from search based methods to more abstract planning techniques however opened up a paradigm for mathematical reasoning on a computer and several systems of that kind now employ a mix of interactive, search based as well as proof planning techniques.The Ωmega system is at the core of several related and well-integrated research projects of the Ωmega research group, whose aim is to develop system support for a working mathematician as well as a software engineer when employing formal methods for quality assurance. In particular, Ωmega supports proof development at a human-oriented abstract level of proof granularity. It is a modular system with a central proof data structure and several supplementary subsystems including automated deduction and computer algebra systems. Ωmega has many characteristics in common with systems like NuPrL, CoQ, Hol, Pvs, and Isabelle. However, it differs from these systems with respect to its focus on proof planning and in that respect it is more similar to the proof planning systems Clam and λClam at Edinburgh.     

E-Science and the data deluge

This paper attempts to show how the “big data” paradigm is changing science through offering access to millions of database elements in real time and the computational power to rapidly process those data in ways that are not initially obvious. In order to gain a proper understanding of these changes and their implications, we propose applying an extended cognition model to the novel scenario.     

Book Notes: Adams,Frederick and Kenneth Aizawa,The Bounds of Cognition,Oxford: Blackwell Publishing, 2008, pp. xiii + 197, AU$120.00 / NZ$130.00 (cloth)

Logical pluralism has been in vogue since JC Beall and Greg Restall 2006 articulated and defended a new pluralist thesis. Recent criticisms such as Priest 2006a Priest, Graham. 2006a. Doubt Truth to be a Liar, Oxford: Oxford University Press.  [Google Scholar] and Field 2009 Field, Hartry. 2009. Pluralism in Logic. Review of Symbolic Logic, 2/2: 342–59. doi:10.1017/S1755020309090182[Crossref], [Web of Science ®] , [Google Scholar] have suggested that there is a relationship between their type of logical pluralism and the meaning-variance thesis for logic. This is the claim, often associated with Quine 1970 Quine, W. V. O. 1970. Philosophy of Logic, Oxford: Oxford University Press.  [Google Scholar], that a change of logic entails a change of meaning. Here we explore the connection between logical pluralism and meaning-variance, both in general and for Beall and Restall's theory specifically. We argue that contrary to what Beall and Restall claim, their type of pluralism is wedded to meaning-variance. We then develop an alternative form of logical pluralism that circumvents at least some forms of meaning-variance.     

Rips的“证明心理学理论”述评

该文对Rips提出的“证明心理学理论”做了综合述评。这一理论主要包含三方面的内容:对推理过程与人类记忆相互关系的解释;(2)根据逻辑学中的“自然推理规则”进行修正后用于解释人类推理过程的推理规则;(3)关于如何控制推理过程的论述。Rips认为他于1983年设计并实施的以“自然推理系统”所含各推理规则为实验材料的实验结果支持该理论的基本观点。     

A general tableau method for propositional interval temporal logics: Theory and implementation

In this paper, we focus our attention on tableau methods for propositional interval temporal logics. These logics provide a natural framework for representing and reasoning about temporal properties in several areas of computer science. However, while various tableau methods have been developed for linear and branching time point-based temporal logics, not much work has been done on tableau methods for interval-based ones. We develop a general tableau method for Venema's CDT logic interpreted over partial orders (BCDT⁺ for short). It combines features of the classical tableau method for first-order logic with those of explicit tableau methods for modal logics with constraint label management, and it can be easily tailored to most propositional interval temporal logics proposed in the literature. We prove its soundness and completeness, and we show how it has been implemented.     

Cut-free common knowledge

Starting off from the infinitary system for common knowledge over multi-modal epistemic logic presented in [L. Alberucci, G. Jäger, About cut elimination for logics of common knowledge, Annals of Pure and Applied Logic 133 (2005) 73–99], we apply the finite model property to “finitize” this deductive system. The result is a cut-free, sound and complete sequent calculus for common knowledge.     

MizarMode—an integrated proof assistance tool for the Mizar way of formalizing mathematics

The Emacs authoring environment for Mizar (MizarMode) is today the authoring tool of choice for many (probably the majority of) Mizar authors. This article describes the MizarMode and focuses on the proof assistance functions and tools available in it.

We start with the explanation of the design principles behind the Mizar system, and show how these design principles—mainly the concentration on simple and intuitive human-oriented proofs—have helped Mizar in developing and maintaining a very large body of formalized mathematics.

Mizar is a non-programmable and non-tactical verifier: the proofs are developed in the traditional “write—compile—correct” software programming loop. While this method is in the beginning more laborious than the methods employed in tactical and programmable proof assistants, it makes the “proof code” in the long-run more readable, maintainable and reusable. This seems to be a crucial factor for a long-term and large-scale formalization effort.

MizarMode has been designed with the aim to facilitate this kind of proof development by a number of “code-generating”, “code-browsing” and “code-searching” methods, and tools programmed or integrated within it. These methods and tools now include, e.g., the automated generation of proof skeletons, semantic browsing of the articles and abstracts, structured viewing, proof advice using trained machine learning tools like the Mizar Proof Advisor, deductive tools like MoMM, etc. We give an overview of these proof-assistance tools and their integration in the MizarMode, and also discuss some emerging and future extensions such as integration of external theorem proving assistance.