Wajsberg algebras and post algebras

We give a presentation of Post algebras of ordern+1 (n1) asn+1 bounded Wajsberg algebras with an additional constant, and we show that a Wajsberg algebra admits a P-algebra reduct if and only if it isn+1 bounded.This autor is partially supported by Grant PB90-0465-C02-01 of D.G.I.C.Y.T. of SpainPresented byJan Zygmunt     

Graded modalities,II (canonical models)

This work intends to be a generalization and a simplification of the techniques employed in [2], by the proposal of a general strategy to prove satisfiability theorems for NLGM-s (= normal logics with graded modalities), analogously to the well known technique of the canonical models by Lemmon and Scott for classical modal logics.     

Dynamic algebras: Examples,constructions, applications

Dynamic algebras combine the classes of Boolean (B 0) and regular (R ; *) algebras into a single finitely axiomatized variety (B R ) resembling an R-module with scalar multiplication . The basic result is that * is reflexive transitive closure, contrary to the intuition that this concept should require quantifiers for its definition. Using this result we give several examples of dynamic algebras arising naturally in connection with additive functions, binary relations, state trajectories, languages, and flowcharts. The main result is that free dynamic algebras are residually finite (i.e. factor as a subdirect product of finite dynamic algebras), important because finite separable dynamic algebras are isomorphic to Kripke structures. Applications include a new completeness proof for the Segerberg axiomatization of prepositional dynamic logic, and yet another notion of regular algebra.Dept. of Computer Science, Stanford, CA 94305 This research was supported by the National Science Foundation under NSF grant no. MCS78-04338. Preparation of the present version was supported by the National Science Foundation under NSF grant number CCR-8814921.This paper originally appeared as Technical Memo #138, Laboratory for Computer Science, MIT, July 1979, and was subsequently revised, shortened, retitled, and published as [Pra80b]. After more than a decade of armtwisting I. Németi and H. Andréka finally persuaded the author to publish TM#138 itself on the ground that it contained a substantial body of interesting material that for the sake of brevity had been deleted from the STOC-80 version. The principal changes here to TM#138 are the addition of footnotes and the sections at the end on retrospective citations and reflections.     

Spatial ontology and physical modalities

Conclusion Most relational theories assert both that spatial discourse is reducible to talk about physical objects and their spatial relations, and that the relation of congruence derives from a non-metrical relation which intervals bear or possibly bear to measuring instruments. We have shown that there are serious logical difficulties involved in maintaining both these positions and the thesis of the continuity of space. We have also shown that Grünbaum's motivating argument for the reduction of congruence is unsound, and, moreover, that the prospects of formulating the kind of definition which this reduction requires seem to rest upon a wholly vague notion of physical possibility. Alternatively, if congruence is taken as primitive, it seems plausible that spatial discourse can be reconstructed so that there is no ontological commitment to spatial objects other than physical objects. Whether or not this relational thesis is ultimately defensible requires more elaboration of the relational theory, and investigation of its role in the formalizations of current physical theories. It is odd, considering the wide currency of relational theories, that this work has never been done.Preparation of this paper was supported in part by a grant from the National Science Foundation (Grant No. SOC75-08464) to the first author.     

Deontic action logic, atomic boolean algebras and fault-tolerance

We introduce a deontic action logic and its axiomatization. This logic has some useful properties (soundness, completeness, compactness and decidability), extending the properties usually associated with such logics. Though the propositional version of the logic is quite expressive, we augment it with temporal operators, and we outline an axiomatic system for this more expressive framework. An important characteristic of this deontic action logic is that we use boolean combinators on actions, and, because of finiteness restrictions, the generated boolean algebra is atomic, which is a crucial point in proving the completeness of the axiomatic system. As our main goal is to use this logic for reasoning about fault-tolerant systems, we provide a complete example of a simple application, with an attempt at formalization of some concepts usually associated with fault-tolerance.     

Factors affecting the filled-duration illusion in the auditory,tactual, and visual modalities

The filled-duration illusion was investigated for auditory, tactual, and visual presentation. The number of intervening discrete elements was the most important factor, as durations with more elements were judged longer than durations with fewer elements. In addition, the configuration of the intervening elements affected judgments. However, the illusion was identical in all three modalities. A cognitive explanation based on counting the number of intervening elements seemed most satisfactory.     

Taste-taste,odor-odor,and taste-odor mixtures: Greater suppression within than between modalities

Subjects judged the intensities of the component qualities of two taste stimuli [sucrose (S) and NaCl (N)], two odor stimuli [citral (C) and anethole (A)], and the mixtures of these stimuli [taste-taste (SN), odor-odor (CA), and taste-odor (SC, NC, SA, and NA)]. The within-modality mixtures, taste-taste and odor-odor, produced greater suppression of perceived intensity than did the between-modality mixtures, taste-odor. However, taste-odor mixtures also produced a significant amount of suppression of perceived intensity when compared with the individual taste and odor stimuli. The data are discussed with respect to peripheral and central mechanisms in mixture suppression.     

Switching of response modalities

When participants perform a sequence of different tasks, it is assumed that the engagement in one task leads to the inhibition of the previous task. This inhibition persists and impairs performance when participants switch back to this (still inhibited) task after only one intermediate trial. Previous task-switching studies on this issue have defined different tasks at the level of stimulus categorization. In our experiments we used different response modalities to define tasks. Participants always used the same stimulus categorization (e.g., categorize a digit as odd vs. even), but had to give a vocal, finger, or foot response (A, B, or C). Our results showed a higher reaction time and error rate in ABA sequences than in CBA sequences, indicating n - 2 repetition cost as a marker for persisting task inhibition. We assume that different response modalities can define a task and are inhibited in a “task switch” in the same way as stimulus categories are inhibited.     

Freudian modalities of disbelief

This article can be characterized as a ‘rediscovery’ of a notion of psychoanalysis that had disappeared or had been confused by later operations. The authors explore a Freudian notion that has been unjustly misunderstood, especially because of the multiple ways in which ‘Unglaube’ – disbelief – has been translated. We shall establish the archaeology of this term in Freud by extracting its three significant modes. Firstly, paranoiac disbelief designates an unconscious process of the rejection of belief in the subject's first encounter with a sexual reality that is always traumatic. Secondly, the obsessional neurotic's disbelief, which we shall call ‘incredulity’, is a secondary, less radical refusal of belief, one that is different from its paranoiac counterpart. Finally, we shall envision a third – dialectical – type of disbelief, which Freud called ‘act of disbelief’ and which will enable us to approach the fundamental epistemic and ethical stakes for psychoanalysis.     

Graded modalities. I

We study a modal system ¯T, that extends the classical (prepositional) modal system T and whose language is provided with modal operators M inn (nN) to be interpreted, in the usual kripkean semantics, as there are more than n accessible worlds such that.... We find reasonable axioms for ¯T and we prove for it completeness, compactness and decidability theorems.The authors are very indebted to the referee for Ms consideration and appreciation of their work.