Partiality and Its Dual

This paper explores allowing truth value assignments to be undetermined or "partial" (no truth values) and overdetermined or "inconsistent" (both truth values), thus returning to an investigation of the four-valued semantics that I initiated in the sixties. I examine some natural consequence relations and show how they are related to existing logics, including ukasiewicz's three-valued logic, Kleene's three-valued logic, Anderson and Belnap's (first-degree) relevant entailments, Priest's "Logic of Paradox", and the first-degree fragment of the Dunn-McCall system "R-mingle". None of these systems have nested implications, and I investigate twelve natural extensions containing nested implications, all of which can be viewed as coming from natural variations on Kripke's semantics for intuitionistic logic. Many of these logics exist antecedently in the literature, in particular Nelson's "constructible falsity".     

A Note on Formality and Logical Consequence

Logic is formal in the sense that all arguments of the same form as logically valid arguments are also logically valid and hence truth-preserving. However, it is not known whether all arguments that are valid in the usual model-theoretic sense are truth-preserving. Tarski claimed that it could be proved that all arguments that are valid (in the sense of validity he contemplated in his 1936 paper on logical consequence) are truth-preserving. But he did not offer the proof. The question arises whether the usual model-theoretic sense of validity and Tarski's 1936 sense are the same. I argue in this paper that they probably are not, and that the proof Tarski had in mind, although unusable to prove that model-theoretically valid arguments are truth-preserving, can be used to prove that arguments valid in Tarski's 1936 sense are truth-preserving.     

An n-Player Semantic Game for an n + 1-Valued Logic

First we show that the classical two-player semantic game actually corresponds to a three-valued logic. Then we generalize this result and give an n-player semantic game for an n + 1-valued logic with n binary connectives, each associated with a player. We prove that player i has a winning strategy in game if and only if the truth value of is t _i in the model M, for 1 ≤ i ≤ n; and none of the players has a winning strategy in if and only if the truth value of is t ₀ in M.     

Valuational semantics of rule derivability

If a certain semantic relation (which we call local consequence) is allowed to guide expectations about which rules are derivable from other rules, these expectations will not always be fulfilled, as we illustrate. An alternative semantic criterion (based on a relation we call global consequence), suggested by work of J.W. Garson, turns out to provide a much better — indeed a perfectly accurate — guide to derivability.     

Ray on Tarski on Logical Consequence

In Logical consequence: A defense of Tarski (Journal of Philosophical Logic, vol. 25, 1996, pp. 617–677), Greg Ray defends Tarski"s account of logical consequence against the criticisms of John Etchemendy. While Ray"s defense of Tarski is largely successful, his attempt to give a general proof that Tarskian consequence preserves truth fails. Analysis of this failure shows that de facto truth preservation is a very weak criterion of adequacy for a theory of logical consequence and should be replaced by a stronger absence-of-counterexamples criterion. It is argued that the latter criterion reflects the modal character of our intuitive concept of logical consequence, and it is shown that Tarskian consequence can be proved to satisfy this criterion for certain choices of logical constants. Finally, an apparent inconsistency in Ray"s interpretation of Tarski"s position on the modal status of the consequence relation is noted.     

Consequence Operations Based on Hypergraph Satisfiability

Four consequence operators based on hypergraph satisfiability are defined. Their properties are explored and interconnections are displayed. Finally their relation to the case of the Classical Propositional Calculus is shown.     

Generalized Logical Consequence: Making Room for Induction in the Logic of Science

We present a framework that provides a logic for science by generalizing the notion of logical (Tarskian) consequence. This framework will introduce hierarchies of logical consequences, the first level of each of which is identified with deduction. We argue for identification of the second level of the hierarchies with inductive inference. The notion of induction presented here has some resonance with Popper's notion of scientific discovery by refutation. Our framework rests on the assumption of a restricted class of structures in contrast to the permissibility of classical first-order logic. We make a distinction between deductive and inductive inference via the notions of compactness and weak compactness. Connections with the arithmetical hierarchy and formal learning theory are explored. For the latter, we argue against the identification of inductive inference with the notion of learnable in the limit. Several results highlighting desirable properties of these hierarchies of generalized logical consequence are also presented.     

A Semantics for Means-end Relations

There has been considerable work on practical reasoning in artificial intelligence and also in philosophy. Typically, such reasoning includes premises regarding means–end relations. A clear semantics for such relations is needed in order to evaluate proposed syllogisms. In this paper, we provide a formal semantics for means–end relations, in particular for necessary and sufficient means–end relations. Our semantics includes a non-monotonic conditional operator, so that related practical reasoning is naturally defeasible. This work is primarily an exercise in conceptual analysis, aimed at clarifying and eventually evaluating existing theories of practical reasoning (pending a similar analysis regarding desires, intentions and other relevant concepts). “They were in conversation without speaking. They didn’t need to speak. They just changed reality so that they had spoken.” Terry Pratchett, Reaper Man     

The Quantitative/Qualitative Watershed for Rules of Uncertain Inference

We chart the ways in which closure properties of consequence relations for uncertain inference take on different forms according to whether the relations are generated in a quantitative or a qualitative manner. Among the main themes are: the identification of watershed conditions between probabilistically and qualitatively sound rules; failsafe and classicality transforms of qualitatively sound rules; non-Horn conditions satisfied by probabilistic consequence; representation and completeness problems; and threshold-sensitive conditions such as ‘preface’ and ‘lottery’ rules. Special Issue Formal Epistemology I. Edited by Branden Fitelson     

Consequence analysis: Its effects on verbal statements about an environmental project

Typically, citizens lack relevant information concerning possible consequences of proposed environmental projects. Despite federal requirements for citizen participation in decisions about proposed roadway projects, no systematic procedures exist for educating citizens as to the possible consequences of such projects. The effects of a consequence analysis procedure on community residents' verbal statements about the favorability of a proposed roadway project were assessed. The consequence analysis procedure involved asking residents to rate the desirability and magnitude of each of 48 possible consequences of the proposed roadway project. Following the intervention, overall ratings of favorability of the project changed for nine of ten residents. Community residents' ratings of the quality of participants' justifications of their position on the roadway issue provided evidence of generalization to this collateral behavior.     

False Though Partly True – An Experiment in Logic

We explore in an experimental spirit the prospects for extending classical propositional logic with a new operator P intended to be interpreted when prefixed to a formula as saying that formula in question is at least partly true. The paradigm case of something which is, in the sense envisaged, false though still partly true is a conjunction one of whose conjuncts is false while the other is true. Ideally, we should like such a logic to extend classical logic – or any fragment thereof under consideration – conservatively, to be closed under uniform substitution (of arbitrary formulas for sentence letters or propositional variables), and to allow the substitutivity of provably equivalent formulas salva provabilitate. To varying degrees, we experience some difficulties only with this last (congruentiality) desideratum in the two four-valued logics we end up giving our most extended consideration to.     

视觉空间关系判断的分离与协同

采用任务表征相互影响范式,通过三个实验探讨了类别空间关系判断和数量空间关系判断的加工特性和相互关系.结果表明:(1)先行类别关系启动有利于数量空间关系判断,对类别空间关系判断没有影响;先行数量关系启动对两个判断任务均无影响.(2)先行类别关系干扰降低两个空间关系判断的绩效,先行数量关系干扰对两个空间关系判断没有影响.(3)先行类别关系对空间关系判断的启动和干扰效应不局限于特定条件,具有普遍性.研究提示,右脑为优势半球的数量关系加工以左脑为优势半球的类别关系加工为基础,支持视觉空间认知加工既分离又协同的观点.     

Identical Twins,Deduction Theorems,and Pattern Functions: Exploring the Implicative BCSK Fragment of S5

We recapitulate (Section 1) some basic details of the system of implicative BCSK logic, which has two primitive binary implicational connectives, and which can be viewed as a certain fragment of the modal logic S5. From this modal perspective we review (Section 2) some results according to which the pure sublogic in either of these connectives (i.e., each considered without the other) is an exact replica of the material implication fragment of classical propositional logic. In Sections 3 and 5 we show that for the pure logic of one of these implicational connectives two – in general distinct – consequence relations (global and local) definable in the Kripke semantics for modal logic turn out to coincide, though this is not so for the pure logic of the other connective, and that there is an intimate relation between formulas constructed by means of the former connective and the local consequence relation. (Corollary 5.8. This, as we show in an Appendix, is connected to the fact that the ‘propositional operations’ associated with both of our implicational connectives are close to being what R. Quackenbush has called pattern functions.) Between these discussions Section 4 examines some of the replacement-of-equivalents properties of the two connectives, relative to these consequence relations, and Section 6 closes with some observations about the metaphor of identical twins as applied to such pairs of connectives.     

Cn-Definitions of Propositional Connectives

We attempt to define the classical propositional logic by use of appropriate derivability conditions called Cn-definitions. The conditions characterize basic properties of propositional connectives.     

Leibniz Filters Revisited

Leibniz filters play a prominent role in the theory of protoalgebraic logics. In [3] the problem of the definability of Leibniz filters is considered. Here we study the definability of Leibniz filters with parameters. The main result of the paper says that a protoalgebraic logic S has its strong version weakly algebraizable iff it has its Leibniz filters explicitly definable with parameters.     

Some Embedding Theorems for Conditional Logic

We prove some embedding theorems for classical conditional logic, covering ‘finitely cumulative’ logics, ‘preferential’ logics and what we call ‘semi-monotonic’ logics. Technical tools called ‘partial frames’ and ‘frame morphisms’ in the context of neighborhood semantics are used in the proof.     

Ranking Alternatives on the Basis of Preference Relations: A Progress Report with Special Emphasis on Outranking Relations

This paper is devoted to the study of techniques allowing one to rank order the elements of a finite set on the basis of a non-necessarily complete or transitive binary relation. In the area of MCDM, such a problem occurs with outranking methods. We review a number of theoretical results concerning this problem and show how they may be useful in order to guide the choice of a particular technique. © 1997 John Wiley & Sons, Ltd.     

论医患关系的法律属性

医事法（又称卫生法）究竟是属于民法的调整范畴还是属于行政法的范畴,国内学术界争议很大。从医学科学与医疗行为的本质特征看,医患关系并不具备民事法律关系所必须具备的主体平等、双方自愿及等价有偿互惠互利三大特征中的任何一个特征。同时也不存在行政主体与行政相对人的关系。为此,首次提出医事法既不调整横向的民事法律关系,也不调整纵向的行政法律关系,而是调整斜向的医事法律关系的一门独立的法律体系的理论。