Discrete tense logic with infinitary inference rules and systematic frame constants: A Hilbert-style axiomatization

The paper deals with the problem of axiomatizing a system 1 of discrete tense logic, where one thinks of time as the set Z of all the integers together with the operations +1 (immediate successor) and -1 (immediate predecessor). 1 is like the Segerberg-Sundholm system W1 in working with so-called infinitary inference rules; on the other hand, it differs from W1 with respect to (i) proof-theoretical setting, (ii) presence of past tense operators and a now operator, and, most importantly, with respect to (iii) the presence in of so-called systematic frame constants, which are meant to hold at exactly one point in a temporal structure and to enable us to express the irreflexivity of such structures. Those frame constants will be seen to play a paramount role in our axiomatization of 1.The present contribution reports research done under the auspices of the Swedish Council for Research in the Humanities and the Social Sciences (HSFR), project On the Legal Concepts of Rights and Duties: an Analysis Based on Deontic and Causal Conditional Logic. I wish to thank the anonymous referee for his/her extremely patient and accurate revision work, and Krister Segerberg for his helpful suggestions.     

A topological logic of action

We consider a quantifier-free language in which there are terms as well as formulas. The proposition-forming propositional operators are the usual ones, and the term-making term operators are the usual lattice theoretical ones. In addition there is a formula-making term operator, does. We study a new logic in which does is claimed to approximate some features of the informal concept the agent performs the action .     

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.     

Matching attidudes towards cartoons across evaluative judgments and nonverbal evaluative behavior

Summary Attitude responses and behavior were theoretically treated as two modalities in a psychophysical matching task. The total response pattern was expected to vary in terms of (a) covariation between modalities and (b) shifts in central tendencies within modalities. Subjects watched a series of humorous and disgusting cartoons on nonsense and women-related topics and evaluated each cartoon using an attitude rating scale. Their facial expressions were secretly videotaped. The tapes were content-analyzed by raters for the amount of nonverbal mirth and of disgust. Independent variables were: (1) Instruction for self-observation (yes/no), (2) Instructions to identify the kind of cartoon (yes/no), (3) Sex of subject (male/female), and (4) Kind of cartoon (nonsense or women-related). The correlation across the total set of cartoons between the two modalities was r=0.88. Self-observation and kind of cartoon affected the strength of covariation of the modalities: sex of subjects and kind of cartoon had a biasing influence on the central tendency of responses.     

Definitions of Gender and Sex: The Subtleties of Meaning

Definitions of the word gender were collected from 137 participants, who also completed questionnaires designed to determine aspects of the usage of the words gender and sex. The majority of participants were European American (86.9%), followed by Latino/a (3.6%), Asian/Asian American (2.9%), African American (2.2%), Native American (1.5%), and West Indian (1.5%). Most participants (70.9%) had attended at least some college and occupations included students (43%), professionals (27.8%), health care workers (4.3%), technical workers (5%), sales and service workers (9.4%), maintenance workers (1.4%), and business owners (1.4%). Data were examined to see which common themes emerged from the free form define gender question, the amount of interchangeability of sex and gender in a sentence completion task, and the varieties of beliefs about the relation between the terms gender and sex. Results indicate a variety of understandings and beliefs about gender that range from the common response that gender is the same as sex to some less common responses that associate gender with females or discrimination. Implications of the ambiguous meaning of gender are discussed with an emphasis on the responsibility of researchers to clarify their own understanding of the terms when they discuss gender or sex in their research and publications.     

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.     

The temporalization of difference: Reflections on Deleuze's interpretation of Bergson

This paper provides an in-depth analysis of Deleuze's interpretation of Bergson, based on his largely ignored 1956 essay, Mergson's Conception of Difference. In this essay, Deleuze first attacks the Hegelian tradition for misunderstanding the notion of difference by reducing it to negation and then uses Bergson's concept of duration – a flow of purely qualitative mental states – to formulate a notion of difference utterly internal to itself, that is, irreducible to negation. The paper argues that this temporalization of difference represents a permanent feature of Deleuze's philosophy – one particularly visible in his highly influential book on Nietzsche – and concludes that Deleuze's Nietzsche therefore appears molded by a Bergsonian imprint.     

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     

The “Big Tent” of Community Psychology: Reactions to Paul Toro’s 2004 Presidential Address

This article summarizes discussions that took place following Paul Toros presidential address for the Society for Community Research and Action (SCRA). Toro argued that community psychology and SCRA are big tents. He suggested growth through increasing the involvement of ethnic minorities, community practitioners, international colleagues, students and early career professionals and individuals from allied disciplines. Themes in the discussions included: the founding values of community psychology, diversity, and social action. Those present felt that the field was facing a mid-life crisis and needed to re-establish its identity. Newer professionals looked to their seasoned colleagues to help define and establish that identity, and involve them in the process. Respondents were supportive of increased involvement of individuals from oppressed groups and practitioners in SCRA. Less attention was paid to increasing the role of international colleagues, professionals from allied disciplines, and members of the community.     

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).     

Care and the dynamics of social world

The concept of social world is formulated for the purpose of deepening our understanding of the dynamics of inclusion, exclusion, and care in interpersonal interaction. World is defined as an irreducible subject-object polarity.Social world is the extremely fragile environment within which people meet, and is easily destroyed. With special attention to family and church life, the conditions for maintaining or losing this environment are examined. Three levels of social world are defined. On the highest level, mutual care, rather than shared opinion, is seen as the factor that facilitates the preservation of social world in the face of world-threatening issues.     

The Deep Structure of Group Life: Unconscious Dimensions

There is a reconsideration and renaissance of interest in expanded conceptions of unconscious processes as they affect individuals and groups (Grotstein, 1999). Recent focus on social unconscious (Hopper, 1996) and cultural unconscious processes (Henderson, 1988) and the nature of intersubjectivity (Harwood and Pines, 1998) raise questions about the location of group analysis. This paper considers the deep structure of group life by examining four functions of the unconscious: repressive, conservative, creative, and mythopoetic (Ellenberger, 1970). On an individual level of analysis, these functions are equated respectively with formative ideas about the: personal–subjective, social–political, intersubjective–cultural and collective–objective unconscious. Group level analogs, as they develop and affect groups and their members, are explored as synthetic, shared, symbolicy and synchronous unconscious processes.     

The elimination of de re formulas

It is shown that de re formulas are eliminable in the modal logic S5 extended with the axiom scheme x x.     

A Translation of Intuitionistic Predicate Logic into Basic Predicate Logic

Basic Predicate Logic, BQC, is a proper subsystem of Intuitionistic Predicate Logic, IQC. For every formula in the language {, , , , , , }, we associate two sequences of formulas 0,1,... and 0,1,... in the same language. We prove that for every sequent , there are natural numbers m, n, such that IQC , iff BQC n m. Some applications of this translation are mentioned.     

Is the holocaust relevant to sociobiology?

Sociobiologists have emphasized that altruism and benevolent behavior are part of the genetic repertoire of most animals and certainly of man. They have constructed a theory of ethics as a biological phenomenon without reference to the concept of evil. It is concluded here however, that holocaust behavior is not equivalent to the natural manifestation of an incompletely tamed animal flashing its teeth. Biologists have been too rigid in trying to equate ethical behavior with social behavior. The added dimension of ethical behavior is a special kind of sensitivity to the needs of others, just as evil is the total lack of it. The evolution of this moral sense may itself have important selective value for the human species, whose survival depends on creating maximal diversity in its gene pool.     

Test of the violation of local realism in quantum mechanics with no use of Bell's inequalities

A novel and versatile polarization-entanglement scheme is adopted to investigate the violation of the EPR local realism for a non-maximally entangled two-photon system according to the recent nonlocality proof by Lucien Hardy. In this context the adoption of a sophisticated detection method allows direct determination of any element of physical reality (viz., determined with probability equal to unity in the words of Einstein, Podolsky and Rosen) for the pair system within complete measurements that are largely insensitive to the detector quantum-efficiencies and noise.     

The group member's view of inner and outer reality: The Janus phenomenon applied to the group

This paper surveys some theoretical aspects of psychodynamic group treatment from the vantage point of the Janus phenomenon. This focus may provide some clarification in understanding how group therapy facilitates growth, especially in the relationships between inner realities and the realities of the external world. The paper explores and seeks bridges and connections between the dynamics of the group and intrapsychic dynamics. The inner view may be understood as intimately connected with intrapsychic concerns, whereas the issues for patients in groups do, to a degree, concern interpersonal processes in and projections onto the external world. The paper concludes that, thus far, we must accept less than perfect integration of theory and settle for limited domain reasoning (Scheidlinger, 1982). Erlebnis is the term coined by Paul Federn (1952) to refer to subjective experience of the self.     

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.     

“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.     

Proof-Theoretic Modal PA-Completeness I: A System-Sequent Metric

This paper is the first of a series of three articles that present the syntactic proof of the PA-completeness of the modal system G, by introducing suitable proof-theoretic objects, which also have an independent interest. We start from the syntactic PA-completeness of modal system GL-LIN, previously obtained in [7], [8], and so we assume to be working on modal sequents S which are GL-LIN-theorems. If S is not a G-theorem we define here a notion of syntactic metric d(S, G): we calculate a canonical characteristic fomula H of S (char(S)) so that _G H (S) and _GL-LIN H, and the complexity of H gives the distance d(S, G) of S from G. Then, in order to produce the whole completeness proof as an induction on this d(S, G), we introduce the tree-interpretation of a modal sequent Q into PA, that sends the letters of Q into PA-formulas describing the properties of a GL-LIN-proof P of Q: It is also a d(*, G)-metric linked interpretation, since it will be applied to a proof-tree T of H with H = char(S) and ( H) = d(S, G).