Inverses for Normal Modal Operators

Given a 1-ary sentence operator , we describe L - another 1-ary operator - as as a left inverse of in a given logic if in that logic every formula is provably equivalent to L. Similarly R is a right inverse of if is always provably equivalent to R. We investigate the behaviour of left and right inverses for taken as the operator of various normal modal logics, paying particular attention to the conditions under which these logics are conservatively extended by the addition of such inverses, as well as to the question of when, in such extensions, the inverses behave as normal modal operators in their own right.     

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     

Supererogation in Deontic Logic: Metatheory for DWE and Some Close Neighbours

In "Doing Well Enough: Toward a Logic for Common Sense Morality", Paul McNamara sets out a semantics for a deontic logic which contains the operator It is supererogatory that. As well as having a binary accessibility relation on worlds, that semantics contains a relative ordering relation, . For worlds u, v and w, we say that u w v when v is at least as good as u according to the standards of w. In this paper we axiomatize logics complete over three versions of the semantics. We call the strongest of these logics DWE for Doing Well Enough.     

Predicate Logics on Display

The paper provides a uniform Gentzen-style proof-theoretic framework for various subsystems of classical predicate logic. In particular, predicate logics obtained by adopting van Behthem's modal perspective on first-order logic are considered. The Gentzen systems for these logics augment Belnap's display logic by introduction rules for the existential and the universal quantifier. These rules for x and x are analogous to the display introduction rules for the modal operators and and do not themselves allow the Barcan formula or its converse to be derived. En route from the minimal modal predicate logic to full first-order logic, axiomatic extensions are captured by purely structural sequent rules.     

On seeing oneself as “left out”: The chronically complaining patient in psychotherapy

A clinical observation regarding patients who complain about feeling left out and/or second best provides the framework for this paper. What is expressed is a form of separation anxiety coupled with a loser self-concept. It is suggested that these patients represent a milder form of the moral masochism. Early theoretical formulations include Freud and his emphasis on the superego and Reich's emphasis on the masochist's fear of being left alone. Kramer's little man phenomenon is an example of a more current theoretical formulation which takes account of the complexities of the ego, and composite self and identity in the clinical phenomena observed. A case of a latency-aged child is provided.     

Cut-free tableau calculi for some propositional normal modal logics

We give sound and complete tableau and sequent calculi for the prepositional normal modal logics S4.04, K4B and G ⁰(these logics are the smallest normal modal logics containing K and the schemata A A, A A and A ( A); A A and AA; A A and ((A A) A) A resp.) with the following properties: the calculi for S4.04 and G ⁰are cut-free and have the interpolation property, the calculus for K4B contains a restricted version of the cut-rule, the so-called analytical cut-rule.In addition we show that G ⁰is not compact (and therefore not canonical), and we proof with the tableau-method that G ⁰is characterised by the class of all finite, (transitive) trees of degenerate or simple clusters of worlds; therefore G ⁰is decidable and also characterised by the class of all frames for G ⁰.Research supported by Fonds zur Förderung der wissenschaftlichen Forschung, project number P8495-PHY.Presented by W. Rautenberg     

The responsive order: A new empiricism

The uniqueness of logic is upheld and contrasted with twenty roles of a wider responsive order that includes us and our procedures. Empirical responses are precise, but different in different approaches. Procedures and findings are independent of (not separable from) their concepts. Two-way feedback obviates a top-down derivation of findings from assumptions, hypotheses, history, or language. The postmodern problems of interpretation, conditions of appearances and relativism involve the ancient error of making perception the model-instance of experience. Instead, bodily interaction functions in language and precedes perception and interpretation. Logic, space time locations and individuated referents involve positional relations derived from comparing. Beyond Kuhn, Feyerabend, Newton and Einstein, if we can give interaction priority over comparing, the responsive objectivity of both can be upheld. A new empiricism, neither naive nor constructivist, uses the words order, explication, truth, and exactly to build on Wittgenstein and on Dilthey's hermeneutic. Natural language is metaphor-like, originally crossed. Logic must ignore its assumptions. It must render everything as a machine and drop humans and animals out. A new discipline is proposed, to move between the logical and the responsive orders, to deal with the machine/human interface and the social uses of science such as bioengineering.     

Synonymous Logics

This paper discusses the general problem of translation functions between logics, given in axiomatic form, and in particular, the problem of determining when two such logics are synonymous or translationally equivalent. We discuss a proposed formal definition of translational equivalence, show why it is reasonable, and also discuss its relation to earlier definitions in the literature. We also give a simple criterion for showing that two modal logics are not translationally equivalent, and apply this to well-known examples. Some philosophical morals are drawn concerning the possibility of having two logical systems that are empirically distinct but are both translationally equivalent to a common logic.     

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).     

Superintuitionistic Companions of Classical Modal Logics

This paper investigates partitions of lattices of modal logics based on superintuitionistic logics which are defined by forming, for each superintuitionistic logic L and classical modal logic , the set L[] of L-companions of . Here L[] consists of those modal logics whose non-modal fragments coincide with L and which axiomatize if the law of excluded middle p V p is added. Questions addressed are, for instance, whether there exist logics with the disjunction property in L[], whether L[] contains a smallest element, and whether L[] contains lower covers of . Positive solutions as concerns the last question show that there are (uncountably many) superclean modal logics based on intuitionistic logic in the sense of Vakarelov [28]. Thus a number of problems stated in [28] are solved. As a technical tool the paper develops the splitting technique for lattices of modal logics based on superintuitionistic logics and ap plies duality theory from [34].     

The artist as transgressor in Mandel'štam's poetry

In Mandel'tam's writing, artistic creativity is described as based on the indispensable yet contradictory modes of compliance and deviation. The artist, by his artistic nature, must be an obedient disciple to the tradition that inspires him, and, at the same time, a violator who renders what inspires him in an individual form. Thus, art implies iterability through novelty. In the totalitarian state, this double nature of art acquires a sinister context and brings the artist to an unavoidable conflict with the state. He has a choice between a servile compliance with the state's command and artistic independence. If the artist complies, he loses his ingenuity; if, on the other hand, he has the courage to break away from the established order, his fate is martyrdom. The criteria of truth and falsehood, the issue of loyalty, of compromise and collaboration or resistance become most relevant. Such words as outcast or non-contemporary acquire the meaning of non-collaborationist or enemy of the people. In the totalitarian state a genuine artist is viewed as a law-breaker, and his art leads him to crime. The notions of compliance and deviation cease being merely aesthetic terms and assume in Mandel'tam's poetry complex, subtle and tragic overtones.I would like to express my gratitude to John Barnstead, Thomas Blakeley, James Doull, Elena Glazov-Corrigan, Gregory Glazov, Leonard Kazdan, Peter Kussmaul, Malcolm Ross, Detlev Steffen, and Ieva Vitins for their valuable criticism, suggestions, and revisions of my English.     

Computer content analysis of sex differences in the language of children

This study presents empirical procedures for the collection and content analysis of the oral language of kindergarten children. The analysis technique used material and machines available to most researchers. The results of the analysis of language samples of 144 randomly selected children from the entire kindergarten class of the Ithaca, New York, school system showed that boys produced significantly more language than did the girls as well as significantly more references to aggression, self, time, space, quantity, fears, good, act of oral communication, negation, and affirmation, and asked more questions of the examiner than did the girls. The girls made significantly more female references than did the boys. Implications for future research are discussed.     

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.     

The Self Psychology of Heinz Kohut: What's It All About Theologically?

As a psychoanalytic thinker who offered by means of his self psychology a new paradigm of psychological development and functioning, Heinz Kohut was also a theologian manqué. With the help of the method of interpretation devised by Paul Tillich and David Tracy, Kohut's limit-concepts of tragic man, the self-object, and empathy, all set within his theory of narcissism, are elucidated as theological constructs. These are critiqued for adequacy from a Christian perspective. The conclusion is that Kohut's understanding of the human dilemma and of the way of salvation correlates well with Christianity, while his view of empathy as the means of salvation has created some confusion. Kohut has thus left an unfinished, profoundly important, agenda for theologians and clinicians.     

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).     

Sets and Classes as Many

In this paper the view is developed that classes should not be understood as individuals, but, rather, as classes as many of individuals. To correlate classes with individuals labelling and colabelling functions are introduced and sets identified with a certain subdomain of the classes on which the labelling and colabelling functions are mutually inverse. A minimal axiomatization of the resulting system is formulated and some of its extensions are related to various systems of set theory, including nonwellfounded set theories.     

Dowód aksjomatyzowalności pewnychn-wartościowych rachunków zdań

Praca ta zostaa wykonana pod kierunkiem prof. drJerzego Supeckiego. Jej szczególny przypadek dotyczcyn-wartociowego rachunku zda o jednej wartoci wyrónionej by referowany w Warszawie na zjedzie Grupy Logiki Instytutu Filozofii i Socjologii PAN. Streszczenie tego referatu [5] zostao wydrukowane w Sprawozdaniach Wydziau Nauk Spoecznych PAN.Allatum est die 19 Aprilis 1963     

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     

Completeness and Decidability Results for Some Propositional Modal Logics Containing “Actually” Operators

The addition of actually operators to modal languages allows us to capture important inferential behaviours which cannot be adequately captured in logics formulated in simpler languages. Previous work on modal logics containing actually operators has concentrated entirely upon extensions of KT5 and has employed a particular model-theoretic treatment of them. This paper proves completeness and decidability results for a range of normal and nonnormal but quasi-normal propositional modal logics containing actually operators, the weakest of which are conservative extensions of K, using a novel generalisation of the standard semantics.