Modal logic with names

We investigate an enrichment of the propositional modal language with a universal modality having semanticsx iff y(y ), and a countable set of names — a special kind of propositional variables ranging over singleton sets of worlds. The obtained language _c proves to have a great expressive power. It is equivalent with respect to modal definability to another enrichment () of, where is an additional modality with the semanticsx iff y(y x y ). Model-theoretic characterizations of modal definability in these languages are obtained. Further we consider deductive systems in _c. Strong completeness of the normal _c-logics is proved with respect to models in which all worlds are named. Every _c-logic axiomatized by formulae containing only names (but not propositional variables) is proved to be strongly frame-complete. Problems concerning transfer of properties ([in]completeness, filtration, finite model property etc.) from to _c are discussed. Finally, further perspectives for names in multimodal environment are briefly sketched.     

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.     

“Soul-making” in a schizophrenic saint

Soul-making (cf. Jung and Hillman) is the process of integrating spiritual and bodily imagery into an intimated wholeness transcending conscious comprehension. Pierre Janet's case of the psychotic mystic, Madeleine, reveals that the patient had been making her own-soul even though his theory had no provision for soul. Janet's soul-stripping theory is contrasted with a soul-making approach, primarily in their respective interpretations of Madeleine's altered states of consciousness. Religious ecstasy is a stretching of soul, an expansion into the realm of spirit, which requires a subsequent descent into and reconciliation with tradition, society, outer world, and body.     

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.     

On regular modal logics with axiom □ ⊤ → □□ ⊤

This paper is devoted to showing certain connections between normal modal logics and those strictly regular modal logics which have as a theorem. We extend some results of E. J. Lemmon (cf. [66]). In particular we prove that the lattice of the strictly regular modal logics with the axiom is isomorphic to the lattice of the normal modal logics.The results in this paper were reported at Logic Colloquium '87 in Granada.     

Some modifications of Scott's theorem on injective spaces

D. Scott in his paper [5] on the mathematical models for the Church-Curry -calculus proved the following theorem.A topological space X. is an absolute extensor for the category of all topological spaces iff a contraction of X. is a topological space of Scott's open sets in a continuous lattice.In this paper we prove a generalization of this theorem for the category of , -closure spaces. The main theorem says that, for some cardinal numbers , , absolute extensors for the category of , -closure spaces are exactly , -closure spaces of , -filters in , >-semidistributive lattices (Theorem 3.5).If = and = we obtain Scott's Theorem (Corollary 2.1). If = 0 and = we obtain a characterization of closure spaces of filters in a complete Heyting lattice (Corollary 3.4). If = 0 and = we obtain a characterization of closure space of all principial filters in a completely distributive complete lattice (Corollary 3.3).     

In and behind a Lenneberg paradigm

Lenneberg suggested that a chimpanzee's linguistic ability could be tested by presenting sentences containing two prepositional phrases joined by a conjunction. This would involve joining two semantic propositions, and thus represents a more complex test of chimpanzee syntactic competence than previously attempted. Jane, a five year-old language trained chimpanzee, was tested on her ability to both produce and comprehend sentences involving a preposition (in or behind) and a conjunction (and). The results from production and comprehension were substantially the same. Jane showed the ability to appropriately deploy and, behind and in, but displayed very little flexibility in their use. It is suggested that a chimpanzee may be able to learn some rules of syntax but is not able to be creative with that syntax.     

On a problem of P(α, δ, π) concerning generalized Alexandroff s cube

Universality of generalized Alexandroff's cube plays essential role in theory of absolute retracts for the category of , -closure spaces. Alexandroff's cube. is an , -closure space generated by the family of all complete filters. in a lattice of all subsets of a set of power .Condition P(, , ) says that is a closure space of all , -filters in the lattice ( ), .Assuming that P (, , ) holds, in the paper [2], there are given sufficient conditions saying when an , -closure space is an absolute retract for the category of , -closure spaces (see Theorems 2.1 and 3.4 in [2]).It seems that, under assumption that P (, , ) holds, it will be possible to givean uniform characterization of absolute retracts for the category of , -closure-spaces.Except Lemma 3.1 from [1], there is no information when the condition P (, , ) holds or when it does not hold.The main result of this paper says, that there are examples of cardinal numbers, , , such that P (, , ) is not satisfied.Namely it is proved, using elementary properties of Lebesgue measure on the real line, that the condition P (, ₁, 2 ) is not satisfied.Moreover it is shown that fulfillment of the condition is essential assumption in, Theorems 2.1 and 3.4 from [1] i.e. it cannot be eliminated.     

Pomiar

Tekst referatu wygoszonego w roku 1957 na konferencji wykadowców logiki w Osiecznej, zorganizowanej przez MSW w zwizku z nowym programem logiki dla przyrodników.Allatum est die 25 Julii 1960     

Rhythm typology of Korean speech

According to their rhythmic properties, spoken languages have been classified by linguists into three categories, i.e. stress-timed, syllable-timed and mora-timed. Recently, this intuitive classification has been confirmed valid with perceptual studies. These studies have shown that both newborn infants and adults, upon hearing the pure rhythms of certain languages, are only able to discriminate between languages of the different categories mentioned above. These results indicate that the capacity of the categorization of the human cognitive system makes possible the classification of language that is not yet explored rhythmically. Here, we investigate the Korean spoken language through the adults discrimination tasks with resynthesized speech. Experimental results indicate that the Korean language is, like Japanese, one of the mora-timed languages.     

Local Theories of Causation and the a Posteriori Identification of the Causal Relation

The need to find an intrinsic characterization of what makes a relation between events causal arises not only in local theories of causation like Salmon's process theory but also in global approaches like Lewis' counterfactual theory. According to the localist intuition, whether a process connecting two events is causal should depend only on what goes on between the events, not on conditions that hold elsewhere in the world. If such intrinsic characterizations could be found, an identification of the causal relation in the actual world (though not in other possible worlds) with physical processes may be feasible (the a posteriori identification). I consider recent proposals made for intrinsic characterizations of causality and conclude that none of them is able to deliver the intended result.     

Gender specificity in value structures

Separate factor analyses of the value rankings of 53 male and 77 female college students yielded three factors for each gender. Interpretation suggested Creative Self-Determination versus Submissive Dependency, Personal Gratification versus Sociopolitical Consciousness, and Existential Responsibility versus Traditionalism as core concepts for the female respondents; while males' axiological dimensions were labeled Communal Idealism versus Entrepreneural Pragmatism, Hedonism versus Egalitarianism, and Sybaritic Bohemianism versus Traditional Sobriety. Each pole of the female factors was interpreted as reflecting a major ideological referent component of the Women's Liberation Movement, while male factors were construed as constituting perspectives for interpreting varieties of response to feminist ideology. Techniques for increasing individuals' levels of self-actualization by direct intervention in axiological organization were discussed.     

Does Alternating Between Masculine and Feminine Pronouns Eliminate Perceived Gender Bias in Text?

This study explores whether alternating betweenthe pronouns he and she ina text is an effective way to avoid sexist language.Participants were psychology students at a largemidwestern university and were predominately White and frommiddle-class backgrounds. Students read two versions ofan essay, one that alternated between masculine andfeminine pronouns and one that exclusively used paired, he or she-type pronouns. Readersperceived the alternating version to be biased in favorof females and lower in overall quality than the pairedversion. However, the alternating version appeared to be more effective at combating sexism,suggesting an alternating strategy may be desirable forauthors with this goal. If the author is not primarilyconcerned with increasing readers' awareness of gender issues, techniques such as pluralization or thesingular they may be moreappropriate.     

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.     

Power,Freedom, and Individuality: Foucault and Sexual Difference

This paper offers a detailed account of Foucaults ethical and political notion of individuality as presented in his late work, and discusses its relationship to the feminist project of the theory of sexual difference. I argue that Foucaults elaboration of the classical ethos of care for the self opens the way for regarding the I-woman as an ethical, political and aesthetic self-creation. However, it has significant limitations that cannot be ignored. I elaborate on two aspects of Foucaults avoidance of sexual difference as a relevant category for an account of political and ethical individuality, which thus implicitly associates individual agency with men. I argue that Foucault implicitly assumes the existence of an ontological desire to become engaged in political self-creation. However, the ethical position of self-knowledge and desire should be understood as a contingent option that depends on material and historical conditions for its realization. Hence, I argue that a feminist reworking of Foucaults notion of political individuality should add a substantial ethical condition to the imperative of self-knowledge and self-creation – making possible the desiring woman subject.     

A Critical Evaluation of Hal Childs' The Myth of the Historical Jesus and the Evolution of Consciousness

The purpose of Childs' book an is integration of historical criticism and analytical psychology. I share Childs' interest in analytical psychology and his concern about the way historical criticism is practiced within the Jesus Seminar. However, I consider his proposed integration to be neither necessary nor desirable, particularly if integration really means amalgamation. Rather than adopting the concerns of analytical psychology, the historical critic would do well to emulate the procedures and rules of evidence of the secular historian.     

Overcoming Self-Negation in Women

The significant overrepresentation of women in depression and a seeming addiction to self-downing are viewed as heavily influenced by internalized gender role messages and further compounded by societal discrimination. The healthy self is defined, and ways of helping women in therapy move toward greater self-acceptance are described, with an emphasis on REBT women's groups. A case study illustrates the process.     

Review article

Conclusions Using the definition of education as a practice, the only coherent interpretation of Heslep's central thesis of Education's moral role was found to need the notion of a social institution of Education. This in turn made sense only by positing a notion such as a Political Proficiency Certificate, with its concomitant drastic government intervention. Heslep himself did not suggest this, presumably because he saw the tension that would appear between such an institution and the voluntary actions of citizens. This tension was then shown to exist even in his notion of the public interest, which brought into question his argument of why Education needs to be standardized. This was reinforced by the realisation that, if the public interest required votes to be aggregated into a social choice, then it is unlikely to be realised by any current voting system. This suggested it was an unsuitable foundation on which to rest either a theory of democracy or a justification for the need for standardized Education. With that justification brought into question, the need for a social institution of Education disappears; without that, as we have said, Heslep's central thesis is without a coherent interpretation.     

Identity in modal logic theorem proving

THINKER is an automated natural deduction first-order theorem proving program. This paper reports on how it was adapted so as to prove theorems in modal logic. The method employed is an indirect semantic method, obtained by considering the semantic conditions involved in being a valid argument in these modal logics. The method is extended from propositional modal logic to predicate modal logic, and issues concerning the domain of quantification and existence in a world's domain are discussed. Finally, we look at the very interesting issues involved with adding identity to the theorem prover in the realm of modal predicate logic. Various alternatives are discussed.     

A new semantical approach to the logic of preference

A possible world semantics for preference is developed. The remainder operator () is used to give precision to the notion that two states of the world are as similar as possible, given a specified difference between them. A general structure is introduced for preference relations between states of affairs, and three types of such preference relations are defined. It is argued that one of them, actual preference, corresponds closely to the concept of preference in informal discourse. Its logical properties are studied and shown to be plausible.