Is “some-other-time” sometimes better than “sometime” for proving partial correctness of programs?

The main result of this paper belongs to the field of the comparative study of program verification methods as well as to the field called nonstandard logics of programs. We compare the program verifying powers of various well-known temporal logics of programs, one of which is the Intermittent Assertions Method, denoted as Bur. Bur is based on one of the simplest modal logics called S5 or sometime-logic. We will see that the minor change in this background modal logic increases the program verifying power of Bur. The change can be described either technically as replacing the reflexive version of S5 with an irreflexive version, or intuitively as using the modality some-other-time instead of sometime. Some insights into the nature of computational induction and its variants are also obtained.This project was supported by the Hungarian National Foundation for Scientific Research, Grant No. 1810.     

A paradigm shift in Heidegger research

The Beiträge zur Philosophie mandates a paradigm shift in Heidegger scholarship. In the face of (1) widespread disarray in the current model, the new paradigm (2) abandons Sein as a name for die Sache selbst, (3) understands Welt/Lichtung/Da as that which gives being, (4) interprets Dasein as apriori openedness rather than as being-there, (5) understands the Kehre as the interface of Geworfenheit and Entwurf, not as a shift in Heidegger's thinking, (6) interprets Ereignis as the opening of the Da rather than as appropriation, and (7) understands human finitude as what gives all forms of being and all epochs in the history of being. The conclusion alludes to the function of Mitdasein (co-openness) as die Sache selbst.     

Understanding the Self in Self-Transcendence

Based on the work of William James and Bernard Lonergan, this article proposes an understanding of the self as a duplex, dialectical, first-person reality constituted by consciousness and experienced as I and me.     

Construction of monadic three-valued Łukasiewicz algebras

The notion of monadic three-valued ukasiewicz algebras was introduced by L. Monteiro ([12], [14]) as a generalization of monadic Boolean algebras. A. Monteiro ([9], [10]) and later L. Monteiro and L. Gonzalez Coppola [17] obtained a method for the construction of a three-valued ukasiewicz algebra from a monadic Boolea algebra. In this note we give the construction of a monadic three-valued ukasiewicz algebra from a Boolean algebra B where we have defined two quantification operations and ^* such that ^*x=^*x (where ^*x=-^*-x). In this case we shall say that and ^* commutes. If B is finite and is an existential quantifier over B, we shall show how to obtain all the existential quantifiers ^* which commute with .Taking into account R. Mayet [3] we also construct a monadic three-valued ukasiewicz algebra from a monadic Boolean algebra B and a monadic ideal I of B. The most essential results of the present paper will be submitted to the XXXIX Annual Meeting of the Unión Matemática Argentina (October 1989, Rosario, Argentina).     

Modal Logics of Succession for 2-Dimensional Integral Spacetime

We consider the problem of axiomatizing various natural successor logics for 2-dimensional integral spacetime. We provide axiomatizations in monomodal and multimodal languages, and prove completeness theorems. We also establish that the irreflexive successor logic in the standard modal language (i.e. the language containing and ) is not finitely axiomatizable.     

Before refraining: Concepts for agency

A structure is described that can serve as a foundation for a semantics for a modal agentive construction such as sees to it that Q ([ stit: Q]). The primitives are Tree,,Instant, Agent, choice. Eleven simple postulates governing this structure are set forth and motivated. Tree and encode a picture of branching time consisting of moments gathered into maximal chains called histories. Instant imposes a time-like ordering. Agent consists of agents, and choice assigns to each agent and each moment in Tree a set of possible choices, where each possible choice is a set of histories. All of these ingredients are referred to in the semantics suggested for [ stit: Q]. The most complex part of the discussion is the motivation for the definition of what it means for a typically non-terminating chain of moments jointly to witness the truth of [ stit: Q] at a moment.The paper begins with an informal account of the Refref conjecture, which says that the only way to refrain from refraining from seeing to something is to see to it. The paper ends with a consideration of an argument of Prior's that in a certain sense contemplation and action are inconsistent.     

A New Representation Theorem for Contranegative Deontic Logic

The logic of an ought operator O is contranegative with respect to an underlying preference relation if it satisfies the property Op & (¬p)(¬q) Oq. Here the condition that is interpolative ((p (pq) q) (q (pq) p)) is shown to be necessary and sufficient for all -contranegative preference relations to satisfy the plausible deontic postulates agglomeration (Op & OqO(p&q)) and disjunctive division (O(p&q) Op Oq).     

Pair discrimination for a continuum of synthetic voiced stops with and without first and third formants

Phoneme labeling and discrimination experiments were conducted with a continuum of voiced stops produced by a Terminal Analog Speech Synthesizer. The stops ranged from |b| to |d|. Only second formant (F₂) transitions changed from one sound to another. (A formant is energy concentrated in a narrow frequency range.) In the labeling experiment conducted to locate the phoneme boundary, subjects identified the individual stimuli as |b| and |d|. In discrimination, difference and identity pairs were presented, with alternative responses of same and different. This allows separate consideration of discrimination (different/Different) and recognition (same/Identity) hits, and also analysis of the data in accordance with the theory of signal detectibility. The sounds were discriminated with and without F ₁ and F ₃ which contained no discriminatory information, but are responsible for perceived similarity to speech. With F ₁ F ₃ , sensitivity (d) was highest at the |b-d| boundary, but without F ₁ F ₃ this was not true. Spectral analysis of the sounds both with and without F ₁ F ₃ revealed a phonemic energy discontinuity for the 1/3 octave around the F ₂ steady-state frequency (1250 Hz). It therefore seems probable that subjects listened to frequencies which contained phonemic information when F ₁ F ₃ were included, but not when they were omitted. In spite of the high sensitivity at the |b-d| boundary, recognition hits (same /Identity) were lowest the boundary had to sound less like a difference to be called different than a pair away from the boundary.Indications, then, are quite strong that auditory-frequency selection helps the perception of speech, and it is clear that a strategy of criterion lowering helps it.     

Maximization of sums of quotients of quadratic forms and some generalizations

Monotonically convergent algorithms are described for maximizing six (constrained) functions of vectors x, or matricesX with columns x₁, ..., x _r . These functions are h₁(x)= _k (xA _kx)(xC _kx)^–1, H₁(X)= _k tr (XA _k X)(XC _k X)^–1, h₁(X)= _{k l} (x _l A _kx _l ) (x _l C _kx _l )^–1 withX constrained to be columnwise orthonormal, h₂(x)= _k (xA _kx)²(xC _kx)^–1 subject to xx=1, H₂(X)= _k tr(XA _kX)(XA_kX)(XC_kX)^–1 subject toXX=I, and h₂(X)= _{k l} (x _l A _kx _l )² (x _l C _kX _l )^–1 subject toXX=I. In these functions the matricesC _k are assumed to be positive definite. The matricesA _k can be arbitrary square matrices. The general formulation of the functions and the algorithms allows for application of the algorithms in various problems that arise in multivariate analysis. Several applications of the general algorithms are given. Specifically, algorithms are given for reciprocal principal components analysis, binormamin rotation, generalized discriminant analysis, variants of generalized principal components analysis, simple structure rotation for one of the latter variants, and set component analysis. For most of these methods the algorithms appear to be new, for the others the existing algorithms turn out to be special cases of the newly derived general algorithms.This research has been made possible by a fellowship from the Royal Netherlands Academy of Arts and Sciences to the author. The author is obliged to Jos ten Berge for stimulating this research and for helpful comments on an earlier version of this paper.     

Axiomatization of the De Morgan type rules

In Section 1 we show that the De Morgan type rules (= sequential rules in L(, ) which remain correct if and are interchanged) are finitely based. Section 2 contains a similar result for L(). These results are essentially based on special properties of some equational theories.     

Hare on utilitarianism and intuitive morality

InMoral Thinking R. M. Hare offers a very influential defense of utilitarianism against intuitive objections. Hare's argument is roughly that utilitarianism conflicts with defensible moral intuitions only in unusual cases and that, in such cases, even defensible moral intuitions are unreliable. This paper reconstructs Hare's arguments and argues that they presuppose the success of his problematic proof of utilitarianism. Contrary to what many have thought, Hare's negative defense of utilitarianism against intuitive objections is not separable from his proof. In the second part of the paper I argue that Hare does not succeed in defending utilitarianism against the objection that it is too demanding. The final section of the paper sketches a substantially revised version of Hare's reply to intuitive objections. So revised, the argument is independent of Hare's proof and affords a plausible answer to the objection that utilitarianism is too demanding.Earlier versions of this paper were presented at Loyola University and Saint Olaf College. I am greatly indebted to my colleague Harry Gensler for helpful comments on numerous drafts of this paper. I would also like to thank Michael Gorr, Brad Hooker, Shelly Kagan, Heidi Malm, Richard Hare, Peter Singer, Onora O'Neill, George Trey, Joe Sullivan, and an anonymous referee. This paper developed out of a series of discussions with Mark Overvold. I dedicate the paper to his memory. I would also like to thank Loyola University for a paid leave of absence which enabled me to write the paper.     

Variations in use of the term “or”

Two studies showed that adults' responses to questions involving the term or varied markedly depending upon the type of question presented. When presented with various objects (A's and B's) and asked to circle all things which are A or B subjects tended to circle A's as well as B's, whereas when asked to circle all the A's or B's subjects showed a relatively stronger tendency to circle one or the other. Moreover the nature of the sets of objects (As and Bs) influenced behavior as well. There was also evidence that the effects due to question wording or set type transferred.     

A partially ordered extention of the integers

This paper presents a monotonic system of Post algebras of order +* whose chain of Post constans is isomorphic with 012 ... -3-2-1. Besides monotonic operations, other unary operations are considered; namely, disjoint operations, the quasi-complement, succesor, and predecessor operations. The successor and predecessor operations are basic for number theory.The editing of this unified version of two previous papers [Epstein, Rasiowa 1990, 1991] by the authors was completed, except for footnotes, while the first author visited at Warsaw University during June–July, 1994. The footnotes were added by the first author in September, 1994.Presented byRyszard Wójcicki     

A reduction rule for Peirce formula

A reduction rule is introduced as a transformation of proof figures in implicational classical logic. Proof figures are represented as typed terms in a -calculus with a new constant P ⁽⁽⁾⁾. It is shown that all terms with the same type are equivalent with respect to -reduction augmented by this P-reduction rule. Hence all the proofs of the same implicational formula are equivalent. It is also shown that strong normalization fails for P-reduction. Weak normalization is shown for P-reduction with another reduction rule which simplifies of (( ) ) into an atomic type.This work was partially supported by a Grant-in-Aid for General Scientific Research No. 05680276 of the Ministry of Education, Science and Culture, Japan and by Japan Society for the Promotion of Science. Hiroakira Ono     

Training Psychologists for a Future in Evolving Health Care Delivery Systems: Building a Better Boulder Model

Recent and dramatic changes in the demand for and reimbursement of psychological services and expertise in health care delivery systems have radical implications for the preparation of psychologists at the predoctoral, internship, and postdoctoral levels. In order to respond to these changes effectively and advance the profession, training programs must realize the expanded and potential role of psychological expertise in evolving health care delivery systems. In this paper, we review several limitations and unfortunate consequences of traditional training programs that have confined the scope of research and practice to the realm of mental health. We propose that future psychologists be recognized and trained from a broader perspective as behavioral scientists, prepared to operate at the highest levels of health care delivery systems. Specific recommendations for training and education are discussed.     

Heidegger's Brightness as a Responsibility of the Therapist in Existential Family Therapy

The author reflects upon the Heideggerian concepts of thrown-ness, death imagery, arrogance and brightness and their usefulness in existential family therapy. The article describes and illustrates with clinical material the process of helping a couple or family to move from an arrogance response to thrownness and death imagery to the response of brightness as attendants of Being. The responsibilities of the therapist in facilitating such a process are also described.Director of the Worthington Logotherapy Institute, co-director of Lantz and Lantz Counseling Associates, and a professor at The Ohio State University. College of Social Work     

Sheaves over Heyting lattices

For a complete Heyting lattice , we define a category Etale (). We show that the category Etale () is equivalent to the category of the sheaves over , Sh(), hence also with -valued sets, see [2], [1]. The category Etale() is a generalization of the category Etale (X), see [1], where X is a topological space.     

Models for stronger normal intuitionistic modal logics

This paper, a sequel to Models for normal intuitionistic modal logics by M. Boi and the author, which dealt with intuitionistic analogues of the modal system K, deals similarly with intuitionistic analogues of systems stronger than K, and, in particular, analogues of S4 and S5. For these prepositional logics Kripke-style models with two accessibility relations, one intuitionistic and the other modal, are given, and soundness and completeness are proved with respect to these models. It is shown how the holding of formulae characteristic for particular logics is equivalent to conditions for the relations of the models. Modalities in these logics are also investigated.This paper presents results of an investigation of intuitionistic modal logic conducted in collaboration with Dr Milan Boi.     

“Some more” notes,toward a “third” sophistic

Historians of rhetoric refer to two Sophistics, one in the 5th century B.C. and another c. 2nd century A.D. Besides these two, there is a 3rd Sophistic, but it is not necessarily sequential. (The 3rd is counter to counting sequentially.) Whereas the representative Sophists of the 1st Sophistic is Protagoras, and the second, Aeschines, the representative sophists of the 3rd are Gorgias (as proto-Third) and Friedrich Nietzsche, Jean-François Lyotard, Michel Foucault, Jacques Lacan, and Paul de Man.To distinguish between and among Socrates, Plato, and Aristotle, and then Protagoras, Gorgias, and Lacan, the author determines how far each of these personages can count. The model of counting, used semiotically across the topoi of possible/impossible, is that of the people of New Guinea: one thing, two things, many things. It is determined (generally) that the philosophers, including Aristotle, count to one; the Sophists to two; and Gorgias, Lacan, and Lyotard, et al. count to many things, thereby breaking up a monism or binarism. The ancient philosophers employ a substratum of probability to hold together the contraries of possible/impossible; the Sophists employ anti/logic, which keeps the contraries/antitheses separate and therefore without synthesis, but which eventually threatens the integrity of the substratum, or the law of non-contradiction; and Gorgias, Lacan, Lyotard et al. theorize about the impossibility/Resistance of the Logos (reason, logic, law, argumentation, history) to Theory/Totalization, because of the Gorgian Kairos and the Lacanian Real — both of which enter the Logos and break up the cycle of the antitheses and create something new, irrational (Untersteiner).This breaking up has a negative/positive influence on Protagoras's man-measure doctrine, which in turn has a similar influence on the problem of the ethical subject. The subject/agent not only no longer knows (by way of Logos) but also no longer acts (as independent agent); the subject becomes a function of Logos as determined by Kairos/Real; it moves from a hypotaxis/syntaxis of one and two to a radical parataxis/paralogy of some more.From the Impossibility/tragedy of knowledge, however, comes the Possible, or Possibilisms, which allows for the new (though divided) ethical subject to reclaim its position as individual. Such a reclamation of the subject, however, has a profound effect on argumentation, and especially the notion of consensus. What is wanted, then, in a Third Sophistic ethical — as opposed to a political — rhetoric is dissensus through radical parataxes and paralogies.     

On sensitive rank tests for comparing the effects of two treatments on a single group

The rank testR _n of Cronholm and Revusky [1965] in effect doubles the number of comparisons carried out in the Mann-Whitney test between Treated and Control subjects chosen from a single group ofn and triples the asymptotic Pitman efficiency against shift alternatives by using a series ofn — 1 subexperiments. However, the full series can be too costly or time-consuming. It is shown thatj appropriately chosen subexperiments will permit one to make at leastj/(j+1) of the number of comparisons possible underR _n, with large sample efficiency ofj/(j+2) relative toR _n against shift alternatives and small sample efficiency greater than that,j=2, 3, ...,n — 2. The resulting test criterion is a sum ofj independent Mann-Whitney test statistics. Its null distribution is tabulated forn10 and small sample efficiency comparisons are carried out forn=10.