The Classification of Propositional Calculi

We discuss Smirnovs problem of finding a common background for classifying implicational logics. We formulate and solve the problem of extending, in an appropriate way, an implicational fragment H of the intuitionistic propositional logic to an implicational fragment TV of the classical propositional logic. As a result we obtain logical constructions having the form of Boolean lattices whose elements are implicational logics. In this way, whole classes of new logics can be obtained. We also consider the transition from implicational logics to full logics. On the base of the lattices constructed, we formulate the main classification principles for propositional logics.     

The Challenge to Affirmative Action

The Bakke case is the latest and most serious challenge to the constitutionality of voluntary affirmative action programs. Bakke, a white male, challenged the constitutionality of the University of California Davis Medical School Special Admissions Program, which admitted 16 minority students with lower objective scores. Although a poor case for Supreme Court review, it was brought before the Court by the Davis Medical School despite the protests of many minority groups. If Bakke is upheld, it could virtually wipe out efforts to include minorities in most professional schools and some government employment.     

The Power of a Propositional Constant

Monomodal logic has exactly two maximally normal logics, which are also the only quasi-normal logics that are Post complete, and they are complete for validity in Kripke frames. Here we show that addition of a propositional constant to monomodal logic allows the construction of continuum many maximally normal logics that are not valid in any Kripke frame, or even in any complete modal algebra. We also construct continuum many quasi-normal Post complete logics that are not normal. The set of extensions of S4.3 is radically altered by the addition of a constant: we use it to construct continuum many such normal extensions of S4.3, and continuum many non-normal ones, none of which have the finite model property. But for logics with weakly transitive frames there are only eight maximally normal ones, of which five extend K4 and three extend S4.     

The Undecidability of Propositional Adaptive Logic

We investigate and classify the notion of final derivability of two basic inconsistency-adaptive logics. Specifically, the maximal complexity of the set of final consequences of decidable sets of premises formulated in the language of propositional logic is described. Our results show that taking the consequences of a decidable propositional theory is a complicated operation. The set of final consequences according to either the Reliability Calculus or the Minimal Abnormality Calculus of a decidable propositional premise set is in general undecidable, and can be -complete. These classifications are exact. For first order theories even finite sets of premises can generate such consequence sets in either calculus.     

Propositional Q-Logic

Topic of the paper is Q-logic – a logic of agency in its temporal and modal context. Q-logic may be considered as a basal logic of agency since the most important stit-operators discussed in the literature can be defined or axiomatized easily within its semantical and syntactical framework. Its basic agent dependent operator, the Q-operator (also known as - or cstit-operator), which has been discussed independently by F. v. Kutschera and B. F. Chellas, is investigated here in respect of its relation to other temporal and modal operators. The main result of the paper, then, is a completeness result for a calculus of Q-logic with respect to a semantics defined on the tree-approach to agency as introduced and developed by, among others, F. v. Kutschera and N. D. Belnap.     

The Intertwinement of Propositional and Doxastic Justification

One important distinction in the debate over the nature of epistemic justification is the one between propositional and doxastic justification. Roughly, while doxastic justification is a property of beliefs, propositional justification is a property of propositions. On a rather common view, which accounts for doxastic justification in terms of propositional justification plus the so-called ‘basing relation’, propositional justification is seen as the prior notion, and doxastic justification is explained in terms of it. According to the opposing view, the direction of explanation needs to be reversed, and doxastic justification should be seen as primary. I distinguish between two notions of priority, and I argue that they give different verdicts with respect to the issue of which notion of justification comes first. The lesson may be taken to be that propositional and doxastic justification are in a relation of intertwinement.     

Propositional quantifiers

Summary In discussing propositional quantifiers we have considered two kinds of variables: variables occupying the argument places of connectives, and variables occupying the argument places of predicates.We began with languages which contained the first kind of variable, i.e., variables taking sentences as substituends. Our first point was that there appear to be no sentences in English that serve as adequate readings of formulas containing propositional quantifiers. Then we showed how a certain natural and illuminating extension of English by prosentences did provide perspicuous readings. The point of introducing prosentences was to provide a way of making clear the grammar of propositional variables: propositional variables have a prosentential character — not a pronominal character. Given this information we were able to show, on the assumption that the grammar of propositional variables in philosopher's English should be determined by their grammar in formal languages (unless a separate account of their grammar is provided), that propositional variables can be used in a grammatically and philosophically acceptable way in philosophers' English. According to our criteria of well-formedness Carnap's semantic definition of truth does not lack an essential predicate - despite arguments to the contrary. It also followed from our account of the prosentential character of bound propositional variables that in explaining propositional quantification, sentences should not be construed as names.One matter we have not discussed is whether such quantification should be called propositional, sentential, or something else. As our variables do not range over (they are not terms) either propositions, or sentences, each name is inappropriate, given the usual picture of quantification. But we think the relevant question in this context is, are we obtaining generality with respect to propositions, sentences, or something else?Because people have argued that all bound variables must have a pronominal character, we presented and discussed in the third section languages in which the variables take propositional terms as substituends. In our case we included names of propositions, that-clauses, and names of sentences in the set of propositional terms. We made a few comparisons with the languages discussed in the second section. We showed among other things how a truth predicate could be used to obtain generality. In contrast, the languages of the second section, using propositional variables, obtain generality without the use of a truth predicate.Special thanks are due to Nuel D. Belnap, Jr., who has given me much valuable assistance with the preparation of this paper. I also thank Alan Ross Anderson, Joseph Camp, Jr., Steven Davis, and Wilfrid Sellars for suggestions and corrections.The preparation of this paper was partly supported by a NSF grant.     

Propositional anaphors

Philosophical Studies - Propositions are posited to perform a variety of explanatory roles. One important role is being what is designated by a dedicated linguistic expression like a that-clause....     

Propositional Names

I propose that an adequate name for a proposition will be (1) rigid, in Kripke’s sense of referring to the same thing in every world in which it exists, and (2) transparent, which means that it would be possible, if one knows the name, to know which object the name refers. I then argue that the Standard Way of naming propositions—prefixing the word ‘that’ to a declarative sentence—does not allow for transparent names of every proposition, and that no alternative naming convention does better. I explore the implications of this failure for deflationism about truth, arguing that any theory that requires the T biconditional to be a priori cannot succeed.     

Propositional discourse logic

A novel normal form for propositional theories underlies the logic pdl, which captures some essential features of natural discourse, independent from any particular subject matter and related only to its referential structure. In particular, pdlallows to distinguish vicious circularity from the innocent one, and to reason in the presence of inconsistency using a minimal number of extraneous assumptions, beyond the classical ones. Several, formally equivalent decision problems are identified as potential applications: non-paradoxical character of discourses, admissibility of arguments in argumentation networks, propositional satisfiability, and the existence of kernels of directed graphs. Directed graphs provide the basis for the semantics of pdl and the paper concludes by an overview of relevant graph-theoretical results and their applications in diagnosing paradoxical character of natural discourses.     

Propositional Attitudes Without Propositions

The most common account of attitude reports is the relational analysis according towhich an attitude verb taking that-clause complements expresses a two-placerelation between agents and propositions and the that-clause acts as an expressionwhose function is to provide the propositional argument. I will argue that a closerexamination of a broader range of linguistic facts raises serious problems for thisanalysis and instead favours a Russellian `multiple relations analysis' (which hasgenerally been discarded because of its apparent obvious linguistic implausibility).The resulting account can be given independent philosophical motivations within anintentionalist view of truth and predication.     

The Lambek Calculus Extended with Intuitionistic Propositional Logic

We present sound and complete semantics and a sequent calculus for the Lambek calculus extended with intuitionistic propositional logic.     

“美学的多样性”:第18届世界美学大会综述

2010年8月9日至13日,美学界的盛会-第18届世界美学大会在北京大学召开,来自国内外的千余名学者参与了这次会议,诚所谓"群贤毕至,少长咸集".本届美学大会的主题为"美学的多样性",由于牵涉议题广泛,参加会议学者众多,本文择其大端,概述如下.     

The Monodic Fragment of Propositional Term Modal Logic

We study term modal logics, where modalities can be indexed by variables that can be quantified over. We suggest that these logics are appropriate for reasoning about systems of unboundedly many reasoners and define a notion of bisimulation which preserves propositional fragment of term modal logics. Also we show that the propositional fragment is already undecidable but that its monodic fragment (formulas using only one free variable in the scope of a modality) is decidable, and expressive enough to include interesting assertions.

     

On The Computational Consequences of Independence in Propositional Logic

Sandu and Pietarinen [Partiality and Games: Propositional Logic. Logic J. IGPL 9 (2001) 101] study independence friendly propositional logics. That is, traditional propositional logic extended by means of syntax that allow connectives to be independent of each other, although the one may be subordinate to the other. Sandu and Pietarinen observe that the IF propositional logics have exotic properties, like functional completeness for three-valued functions. In this paper we focus on one of their IF propositional logics and study its properties, by means of notions from computational complexity. This approach enables us to compare propositional logic before and after the IF make-over. We observe that all but one of the best-known decision problems experience a complexity jump, provided that the complexity classes at hand are not equal. Our results concern every discipline that incorporates some notion of independence such as computer science, natural language semantics, and game theory. A corollary of one of our theorems illustrates this claim with respect to the latter discipline.