Pooling Modalities and Pointwise Intersection: Semantics,Expressivity, and Dynamics

Journal of Philosophical Logic - We study classical modal logics with pooling modalities, i.e. unary modal operators that allow one to express properties of sets obtained by the pointwise...     

Containment Logics: Algebraic Completeness and Axiomatization

Studia Logica - The paper studies the containment companion (or, right variable inclusion companion) of a logic $$\vdash $$ . This consists of the consequence relation $$\vdash ^{r}$$ which...     

Axiomatization and completeness of uncountably valued approximation logic

A first order uncountably valued logicL _Q(0,1) for management of uncertainty is considered. It is obtained from approximation logicsL _T of any poset type (T, ) (see Rasiowa [17], [18], [19]) by assuming (T, )=(Q(0, 1), ) — whereQ(0, 1) is the set of all rational numbersq such that 0<q<1 and is the arithmetic ordering — by eliminating modal connectives and adopting a semantics based onLT-fuzzy sets (see Rasiowa and Cat Ho [20], [21]). LogicL _Q(0,1) can be treated as an important case ofLT-fuzzy logics (introduced in Rasiowa and Cat Ho [21]) for (T, )=(Q(0, 1), ), i.e. asLQ(0, 1)-fuzzy logic announced in [21] but first examined in this paper.L _Q(0,1) deals with vague concepts represented by predicate formulas and applies approximate truth-values being certain subsets ofQ(0, 1). The set of all approximate truth-values consists of the empty set ø and all non-empty subsetss ofQ(0, 1) such that ifqs andqq, thenqs. The setLQ(0, 1) of all approximate truth-values is uncountable and covers up to monomorphism the closed interval [0, 1] of the real line.LQ(0, 1) is a complete set lattice and therefore a pseudo-Boolean (Heyting) algebra. Equipped with some additional operations it is a basic plain semi-Post algebra of typeQ(0, 1) (see Rasiowa and Cat Ho [20]) and is taken as a truth-table forL _Q(0,1) logic.L _Q(0,1) can be considered as a modification of Zadeh's fuzzy logic (see Bellman and Zadeh [2] and Zadeh and Kacprzyk, eds. [29]). The aim of this paper is an axiomatization of logicL _Q(0,1) and proofs of the completeness theorem and of the theorem on the existence ofLQ(0, 1)-models (i.e. models under the semantics introduced) for consistent theories based on any denumerable set of specific axioms. Proofs apply the theory of plain semi-Post algebras investigated in Cat Ho and Rasiowa [4].Presented byCecylia Rauszer     

College Counseling: Union and Intersection

College counseling can best be understood as the intersection of a professional activity and an environment. The specialty has developed from the merging of several movements: vocational guidance, mental health, and student personnel work. These elements are reflected in the diversity of backgrounds and perspectives represented by college counselors and in differing models of counseling services. College counseling will be affected by trends including health care reform, scarcity of resources in higher education, changing student demographics, and complex societal issues.     

Art Media and the Sense Modalities: Tactile Pictures

It is widely assumed that the art media can be individuated with reference to the sense modalities. Different art media are perceived by means of different sense modalities, and this tells us what properties of each medium are aesthetically relevant. The case of pictures appears to fit this principle well, for pictures are deemed purely and paradigmatically visual representations. However, recent psychological studies show that congenitally and early blind people have the ability to interpret and make raised-line drawings through touch. This shows that pictures are not essentially visual representations. The view that pictures are essentially visual follows from influential views of the nature of depiction and of the nature of vision that are mistaken. By rooting out the mistake, we learn something about pictures, something about vision, and something about the doctrine that art media are individuated by the sense modalities.     

Pooling peripheral information: Averages versus extreme values

Suppose, as an idealization, that sensory intensity is coded in peripheral channels as identical Poisson pulse trains with intensity parameter a power function of signal intensity. Discrimination models based on either an average count computed over a fixed time or an average time computed for a fixed count per channel have difficulty in fitting the Weber function ($\text{ΔI}\text{I}$ versus I) if the free parameters are constrained to ranges determined from other experiments (magnitude estimation, reaction time). Here we study a different decision rule, namely, the most extreme observation in either the counting or timing mode. Our extremum-counting model, but not two timing ones, accounts very nicely for the Weber function. However, the ROC curves for these extremum models, which agree in shape with data of Green and Luce, yield estimates for the intensity parameter which are much larger than predicted by the power function growth used to calculate ΔI and about twice as large as those estimated from reaction time data collected in the same experiment.     

Non-Adjunctive Inference and Classical Modalities

The article focuses on representing different forms of non-adjunctive inference as sub-Kripkean systems of classical modal logic, where the inference from □A and □B to □A∧B fails. In particular we prove a completeness result showing that the modal system that Schotch and Jennings derive from a form of non-adjunctive inference in (Schotch and Jennings, 1980) is a classical system strictly stronger than EMN and weaker than K (following the notation for classical modalities presented in Chellas, 1980). The unified semantical characterization in terms of neighborhoods permits comparisons between different forms of non-adjunctive inference. For example, we show that the non-adjunctive logic proposed in (Schotch and Jennings, 1980) is not adequate in general for representing the logic of high probability operators. An alternative interpretation of the forcing relation of Schotch and Jennings is derived from the proposed unified semantics and utilized in order to propose a more fine-grained measure of epistemic coherence than the one presented in (Schotch and Jennings, 1980). Finally we propose a syntactic translation of the purely implicative part of Jaśkowski's system D₂ into a classical system preserving all the theorems (and non-theorems) explicilty mentioned in (Jaśkowski, 1969). The translation method can be used in order to develop epistemic semantics for a larger class of non-adjunctive (discursive) logics than the ones historically investigated by Jaśkowski.     

Some Results on Modal Axiomatization and Definability for Topological Spaces

We consider two topological interpretations of the modal diamond—as the closure operator (C-semantics) and as the derived set operator (d-semantics). We call the logics arising from these interpretations C-logics and d-logics, respectively. We axiomatize a number of subclasses of the class of nodec spaces with respect to both semantics, and characterize exactly which of these classes are modally definable. It is demonstrated that the d-semantics is more expressive than the C-semantics. In particular, we show that the d-logics of the six classes of spaces considered in the paper are pairwise distinct, while the C-logics of some of them coincide. Mathematics Subject Classifications (2000): 03B45, 54G99. Presented by Michael Zakharyaschev     

Interaction Across Modalities: I. Successive Stimulation

The aim of the study was to determine the structure and dimensionality of social-political attitudes. Also investigated was the hypothesis that the liberal vs. conservative attitude dimension was synonymous with the value dimension rule free vs. authoritarian. An attitude measure consisting of simply stated social-political issues and a personal values inventory were administered to a varied sample of 300 men and women. Analysis of the attitude items disclosed three factors—Liberal vs. Conservative, Freedom of Sex Expression, and Equalitarianism—whose intercorrelations indicated a common dimension of conservatism. The cross-correlations in both the male and female samples support the hypothesis that conservative attitudes and authoritarian values were essentially identical constructs. Groups ranked by conservativism and groups ranked as to age increased significantly in mean conservativism score as anticipated.     

Testimony as Evidence: More Problems for Linear Pooling

This paper considers a special case of belief updating??when an agent learns testimonial data, or in other words, the beliefs of others on some issue. The interest in this case is twofold: (1) the linear averaging method for updating on testimony is somewhat popular in epistemology circles, and it is important to assess its normative acceptability, and (2) this facilitates a more general investigation of what it means/requires for an updating method to have a suitable Bayesian representation (taken here as the normative standard). The paper initially defends linear averaging against Bayesian-compatibility concerns raised by Bradley (Soc Choice Welf 29:609?C632, 2007), as well as problems associated with multiple testimony updates. The resolution of these issues, however, requires an extremely nuanced interpretation of the parameters of the linear averaging model??the so-called weights of respect. We go on to propose a role that the parameters of any ??shortcut?? updating function should play, by way of minimal interpretation of these parameters. The class of updating functions that is consistent with this role, however, excludes linear averaging, at least in its standard form.     

From Outcomes to Acts: A Non-Standard Axiomatization of the Expected Utility Principle

This paper presents an axiomatization of the principle of maximizing expected utility that does not rely on the independence axiom or sure-thing principle. Perhaps more importantly the new axiomatization is based on an ex ante approach, instead of the standard ex post approach. An ex post approach utilizes the decision maker's preferences among risky acts for generating a utility and a probability function, whereas in the ex ante approach a set of preferences among potential outcomes are on the input side of the theory and the decision maker's preferences among risky acts on the output side.     

A Structural Blueprint for Group Facilitators: Three Group Modalities

This article provides a conceptual model, typology, or blueprint to unify and more clearly understand the spectrum of task-, socio-, and psycho-group processes used by guidance and counseling personnel. The authors provide a structure for group leaders to follow within their various group forms or modalities.     

Nested Deontic Modalities: Another View of Parking on Highways

A suggestion is made for representing iterated deontic modalities in stit theory, the “seeing-to-it-that” theory of agency. The formalization is such that normative sentences are represented as agentive sentences and therefore have history dependent truth conditions. In contrast to investigations in alethic modal logic, in the construction of systems of deontic logic little attention has been paid to the iteration... of the deontic modalities. L. Goble (1966, p. 197) N. Belnap and P. Bartha (1995) present a formalization of iterated deontic modalities in stit theory, the “seeing-to-it-that” theory of agency, due to Belnap, Perloff, and Xu (1996). In the present paper a simplification of Belnap and Bartha's approach is suggested. In order to support easy comparison with (1995), I shall take up Belnap and Bartha's discussion of R. Barcan Marcus' (1966) example Parking on highways ought to be forbidden. The simplified account underlines the power of stit theory and represents obligations, prohibitions and permissions as agentive sentences, as required by iteration. Therefore, in particular, the truth of obligations, prohibitions and permissions is it history dependent. This revised version was published online in July 2006 with corrections to the Cover Date.