分布逻辑的理论与分析

以往的逻辑理论讨论的是理论上命题之间的逻辑关系,作为一种基本准则,可以放在许多情况下使用,但是一般的逻辑理论相对抽象,命题形式过于简单,这样有时不能很准确很方便地处理实际问题,在传统数学中,分布是一种重要的思想,基于这种思想建立了分布逻辑理论,同时对命题值在分布结构上的真假以及变化进行了讨论。     

The Place of Logic in Reasoning

Reasoning is a goal-oriented activity. The logical steps are at best the median part of a full reasoning: before them, a language has to be defined, and a model of the goal in this language has to be developed; after them, their result has to be checked in the real world with respect to the goal. Both the prior and the subsequent steps can be conducted rationally; none of them has a logical counterpart. Furthermore, Logic aims at prescribing what a correct reasoning is. But correct with respect to what? If the answer is: with respect to truth, the next question is whether the truth in everyday life, physics, economy, is the same as the truth that logicians have in mind. Resorting to Logic is justified only if an idealization in terms of true propositions in the logical sense is compatible with the goal. If such an idealization is legitimate, so is the use of classical Logic. If not, there is no authority forbidding to skew Logic in order to better reflect the nature of the reasoning required for the task.     

Lukasiewicz n值命题逻辑中命题的真度理论

利用势为 n的均匀概率空间的无穷乘积在 Lukasiewicz n值命题逻辑中引入了公式的真度概念,当3≤n≤17时证明了全体公式的真度值之集在[0,1]上是稠密的,并给出了公式真度的表达通式;利用真度定义了公式间的相似度,进而导出了全体公式集上的一种伪距离,为n值Lukasiewicz命题逻辑系统的近似推理理论提供了一种可能的框架。     

Lukasiewicz三值命题逻辑中命题的真度理论

利用势为3的均匀概率空间的无穷乘积在Lukasiewicz三值命题逻辑中引入了公式的真度概念，证明了全体公式的真度值之集在[0，1]上是稠密的，并给出真度的表达式；利用真度定义公式问的相似度，进而导出全体公式集上的一种伪距离，为三值命题的近似推理理论提供一种可能的框架。     

Actualism and Modal Semantics

According to actualism, modal reality is constructed out of valuations (combinations of truth values for all propositions). According to possibilism, modal reality consists in a set of possible worlds, conceived as independent objects that assign truth values to propositions. According to possibilism, accounts of modal reality can intelligibly disagree with each other even if they agree on which valuations are contained in modal reality. According to actualism, these disagreements (possibilist disagreements) are completely unintelligible. An essentially actualist semantics for modal propositional logic specifies which sets of valuations are compatible with the meanings of the truth-functional connectives and modal operators without drawing on formal resources that would enable us to represent possibilist disagreements. The paper discusses the availability of an essentially actualist semantics for modal propositional logic. I argue that the standard Kripkean semantics is not essentially actualist and that other extant approaches also fail to provide a satisfactory essentially actualist semantics. I end by describing an essentialist actualist semantics for modal propositional logic.     

逻辑系统$G_3$中命题的真度值之集在[0,1]上的分布

利用势为3的均匀概率空间的无穷乘积在G■del三值命题逻辑中引入了公式的真度概念,给出了真度推理规则,证明了全体公式的真度值之集在[0,1]上是稠密的,并给出了公式真度的表达通式,为进一步建立三值命题逻辑的近似推理理论奠定了基础．     

Triangles, Schemes and Worlds: Reply to Nulty

Nulty proposes a “Davidsonian” argument for metaphysical pluralism, the thesis that there are (or could be) many actual worlds, which appeals to the possibility of alien forms of triangulation. I dispute Nulty’s reading of Davidson on two important points: Davidson’s attack on the notion of a conceptual scheme is not, as Nulty thinks, directed at pluralism, and his understanding of the notions of objective truth and reality is at odds with the conception needed for Nulty’s argument. I also show that the pluralist argument fails on its own terms as it requires an assimilation of worlds to worldviews. But there is much of value in Nulty’s paper despite these important flaws. When the confusions are cleared up, we are left with an intriguing and novel line of argument for conceptual relativism.     

Resolution vs. cutting plane solution of inference problems: Some computational experience

Resolvents in the propositional calculus correspond to certain cutting planes in integer programming models of inference problems. We compare the performance of a rudimentary cutting plane algorithm that uses only resolvents as cuts with that of ‘set-of-support’ resolution on random inference problems. The cutting plane algorithm is orders of magnitude faster on problems in which the premises do not imply the given proposition (i.e., the majority of random problems), and moderately faster on other random problems.     

Is There a Conceptual Connection Between Intentionality and Consciousness?

It is argued that Searle’s argument for the thesis that there is a conceptual connection between intentionality and consciousness suffers from serious ambiguities. Searle’s argument is reconstructed as consisting of three premises that contain the notions of aspectual shape and irreducible subjectivity. Having identified two different readings of ‘aspectual shape’ and ‘irreducibly subjective,’ I conclude that each version of Searle’s argument incorporates at least one false premise. This paper is a descendant of a paper presented at the Wittgenstein Symposium at Kirchberg am Wechsel in August 2004. I would like to thank the reviewer of this journal for his/her helpful comments on a previous draft.     

Knowledge,Assertion, and Inference

This paper argues that three plausible principles are mutually inconsistent: (KA) One ought to assert only what one knows; (AP) If it is proper to assert some proposition q, then it is, barring special and not very common circumstances, proper to assert any proposition p from which q has been competently inferred; and (AKN) Some propositions are both properly assertible and known by competent inference from propositions which one does not know. Each pair of two principles constitutes an argument against the remaining principle, but which principle should one drop?     

Probability,fuzziness and borderline cases

An integrated approach to truth-gaps and epistemic uncertainty is described, based on probability distributions defined over a set of three-valued truth models. This combines the explicit representation of borderline cases with both semantic and stochastic uncertainty, in order to define measures of subjective belief in vague propositions. Within this framework we investigate bridges between probability theory and fuzziness in a propositional logic setting. In particular, when the underlying truth model is from Kleene's three-valued logic then we provide a complete characterisation of compositional min–max fuzzy truth degrees. For classical and supervaluationist truth models we find partial bridges, with min and max combination rules only recoverable on a fragment of the language. Across all of these different types of truth valuations, min–max operators are resultant in those cases in which there is only uncertainty about the relative sharpness or vagueness of the interpretation of the language.     

标准序列逻辑系统S_3中公式的概率真度理论

利用势为3的非均匀概率空间的无穷乘积在三值标准序列逻辑系统中引入了公式的概率真度概念,证明了全体公式的概率真度值之集在[0,1]中没有孤立点;利用概率真度定义了概率相似度和伪距离,进而建立了概率逻辑度量空间,证明了该空间中没有孤立点,为三值命题的近似推理理论提供了一种可能的框架.     

Conceptual Schemes Revisited: Davidsonian Metaphysical Pluralism

Davidson’s 1974 argument denying the possibility of incommensurable conceptual schemes is widely interpreted as entailing a denial of metaphysical pluralism. Speakers may group objects differently or have different beliefs about the world, but there is just one world. I argue there is tension arising from three aspects of Davidson’s philosophy: (1) the 1974 argument against conceptual schemes; (2) Davidson’s more recent emphasis on primitive triangulation as a necessary condition for thought and language; and (3) Davidson’s semantic approach to metaphysics, what he calls ‘the method of truth in metaphysics’. After elucidating the tension, I argue the tension can be resolved while preserving at least two major tenets of Davidson’s philosophy: (1) conceptual schemes do not carve an uninterpreted reality into different worlds and (2) truth is objective and non-epistemic. I argue Davidson is implicitly committed to a plurality of worlds.     

Things That are Right with the Traditional Square of Opposition

The truth conditions that Aristotle attributes to the propositions making up the traditional square of opposition have as a consequence that a particular affirmative proposition such as ‘Some A is not B’ is true if there are no Bs. Although a different convention than the modern one, this assumption remained part of centuries of work in logic that was coherent and logically fruitful.      

Can realists know that they know?

Realists typically suppose that nonepistemic truth is an independent condition on propositional knowledge. Few philosophers, however, have seriously questioned the meta-epistemic consequences of combining alethic and epistemic variants of realism. In this paper I aim to show that the truth condition in the customary definition of knowledge presents an important problem for the realist at higher epistemic levels. According to my argument, traditional epistemic-logical analyses of metaknowledge fail because of their extensionalism and certain presuppositions they have about the satisfaction of the truth condition. I further suggest that we need a different approach to metaknowledge if (1) we want to retain alethic realism, and (2) we want our epistemological accounts to adequately explicate the meta-epistemic states of actual, evidence-bound cognitive agents. This paper greatly benefited from the comments and criticisms of an anonymous referee for Acta Analytica.     

具有有穷个模态辞的模态系统

<正> 在真值逻辑系统中如果加入“可能”“必然”等模熊概念,所得的逻辑系统叫做模态系统(modal system).如果该真值系就为伟统的二值系统,特名曰传统模态系统(下文的讨论不限于传统模态系统).纯由命题变元以及“～”(非)“◇”(可能)“口”(必然)三运算而组成的命题叫做模态辞(modality).若只经奇数次～运算的名曰负模态辞,经偶数次(包括0次)～运算的名曰正模态辞.     

On the recognition of the tautological nature of propositional formulas

A formal language whose propositions express (in some sense) the properties of propositional formulas is described in the paper. For a certain subset of propositions of this language it is proved that each of them defines a class of propositional formulas, on which it is possible to recognize the tautological nature in a time polynomially dependent on the formula's length.Translated fromZapiski Nauchnykh Seminarov Leningradskogo Matematicheskogo, Otdeleniyaim. V. A.Steklova Akad.Nauk SSSR, Vol. 60, pp. 197–206,1976. Result announced December 4, 1974.     

Explanation, Entailment, and Leibnizian Cosmological Arguments

I argue that there are Leibnizian-style cosmological arguments for the existence of God which start from very mild premises which affirm the mere possibility of a principle of sufficient reason. The utilization of such premises gives a great deal of plausibility to such types of argumentation. I spend the majority of the paper defending three major objections to such “mild” premises viz., a reductio argument from Peter van Inwagen and William Rowe, which proffers and defends the idea that a necessary proposition cannot explain a contingent one. I, then, turn to an amelioration of the Rowe/van Inwagen argument which attempts to appeal to an entailment relation between explanans and explanandum that is fettered out in terms of relevance logic. Subsequent to dispelling with that worry, I tackle objections to the utilization of weak principles of sufficient reason that depend essentially upon agglomerative accounts of explanation.     

How mathematical impossibility changed welfare economics: A history of Arrow's impossibility theorem

During the 20th century, impossibility theorems have become an important part of mathematics. Arrow's impossibility theorem (1950) stands out as one of the first impossibility theorems outside of pure mathematics. It states that it is impossible to design a welfare function (or a voting method) that satisfies some rather innocent looking requirements. Arrow's theorem became the starting point of social choice theory that has had a great impact on welfare economics. This paper will analyze the history of Arrow's impossibility theorem in its mathematical and economic contexts. It will be argued that Arrow made a radical change of the mathematical model of welfare economics by connecting it to the theory of voting and that this change was preconditioned by his deep knowledge of the modern axiomatic approach to mathematics and logic.