Expansion and Contraction of Finite States

We present a theory that copes with the dynamics of inconsistent information. A method is set forth to represent possibly inconsistent information by a finite state. Next, finite operations for expansion and contraction of finite states are given. No extra-logical element — a choice function or an ordering over (sets of) sentences — is presupposed in the definition of contraction. Moreover, expansion and contraction are each other's duals. AGM-style characterizations of these operations follow.     

Vagueness and Blurry Sets

This paper presents a new theory of vagueness, which is designed to retain the virtues of the fuzzy theory, while avoiding the problem of higher-order vagueness. The theory presented here accommodates the idea that for any statement S ₁ to the effect that Bob is bald is x true, for x in [0,1], there should be a further statement S ₂ which tells us how true S ₁ is, and so on – that is, it accommodates higher-order vagueness – without resorting to the claim that the metalanguage in which the semantics of vagueness is presented is itself vague, and without requiring us to abandon the idea that the logic – as opposed to the semantics – of vague discourse is classical. I model the extension of a vague predicate P as a blurry set, this being a function which assigns a degree of membership or degree function to each object o, where a degree function in turn assigns an element of [0,1] to each finite sequence of elements of [0,1]. The idea is that the assignment to the sequence 0.3,0.2, for example, represents the degree to which it is true to say that it is 0.2 true that o is P to degree 0.3. The philosophical merits of my theory are discussed in detail, and the theory is compared with other extensions and generalisations of fuzzy logic in the literature.     

A Grim Semantics For Logics of Belief

Patrick Grim has presented arguments supporting the intuition that any notion of a totality of truths is incoherent. We suggest a natural semantics for various logics of belief which reflect Grim’s intuition. The semantics is a topological semantics, and we suggest that the condition can be interpreted to reflect Grim’s intuition. Beyond this, we present a natural canonical topological model for K4 and KD4.     

An Early Buddhist Text on Logic: Fang Bian Xin Lun

The Fang Bian Xin Lun is a text on Buddhist logic which is thought to be the earliest one still to be extant. It appears in Chinese only (T1632). The great Italian indologist Giuseppe Tucci, believing that the text was originally a Sanskrit text, translated it into Sanskrit and gave it the title Upāyahṛdaya. The paper provides the historical background of the development of logic in Classical India up to the time of this text, summarizes its content and translates its first section.

Combining Possibilities and Negations

Combining non-classical (or sub-classical) logics is not easy, but it is very interesting. In this paper, we combine nonclassical logics of negation and possibility (in the presence of conjunction and disjunction), and then we combine the resulting systems with intuitionistic logic. We will find that Kracht's results on the undecidability of classical modal logics generalise to a non-classical setting. We will also see conditions under which intuitionistic logic can be combined with a non-intuitionistic negation without corrupting the intuitionistic fragment of the logic.     

《易经》:人类科学思维和审美思维方式的精典阐释

一本诞生于五千年前的中国古书《易经》,已经包含着深刻的现代科学数理逻辑原理,且与美学的审美逻辑原理互为支持、互为表里,使这两大类本来被认为水火不相容的领域及其独具的思维方式得到了高度完善统一的阐释。从这样的角度来看《易经》,也许会有助于目前心理学界对思维方式及逻辑问题的研究,拓开一条崭新的思路。     

On Different Intuitionistic Calculi and Embeddings from Int to S4

In this paper, we compare several cut-free sequent systems for propositional intuitionistic logic Intwith respect to polynomial simulations. Such calculi can be divided into two classes, namely single-succedent calculi (like Gentzen's LJ) and multi-succedent calculi. We show that the latter allow for more compact proofs than the former. Moreover, for some classes of formulae, the same is true if proofs in single-succedent calculi are directed acyclic graphs (dags) instead of trees. Additionally, we investigate the effect of weakening rules on the structure and length of dag proofs.The second topic of this paper is the effect of different embeddings from Int to S4. We select two different embeddings from the literature and show that translated (propositional) intuitionistic formulae have sometimes exponentially shorter minimal proofs in a cut-free Gentzen system for S4than the original formula in a cut-free single-succedent Gentzen system for Int. Moreover, the length and the structure of proofs of translated formulae crucially depend on the chosen embedding.     

On the Nature of Continuous Physical Quantities in Classical and Quantum Mechanics

Journal of Philosophical Logic - Within the traditional Hilbert space formalism of quantum mechanics, it is not possible to describe a particle as possessing, simultaneously, a sharp position value...     

The ad Hominem argument as an informal fallacy

This article outlines criteria for the evaluation of the argumentum ad hominem (argument against the person, or personal attack in argument) that is traditionally a part of the curriculum in informal logic. The argument is shown to be a kind of criticism which works by shifting the burden of proof in dialogue through citing a pragmatic inconsistency in an arguer's position. Several specific cases of ad hominem argumentation which pose interesting problems in analyzing this type of criticism are studied.