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.     

Strict embedding of the elementary ontology into the monadic second-order calculus of predicates admitting the empty individual domain

There is given the proof of strict embedding of Leniewski's elementary ontology into monadic second-order calculus of predicates providing a formalization of the class of all formulas valid in all domains (including the empty one). The elementary ontology with the axiom S (S S) is strictly embeddable into monadic second-order calculus of predicates which provides a formalization of the classes of all formulas valid in all non-empty domains.     

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.     

B. “Verification” of statements in psychiatry

(1) It remains to be seen if in the field of Psychiatry just as in that of Psychology the verbal output of a subject can be submitted to verification. Many statements of a highly emotional character being merely symptoms of certain dispositions have no direct communicative sense at all.(2) It being one of the characteristics of the mentally ill to loose contact and exchange of ideas with other people, the question naturally suggests itself if this symptom may be at the bottom of the phenomenon of these persons taking refuge in logical and ideological terminologies, their talk being a kind of verbal autism.(3) The expression verbal autism is used here for statements on a purely subjective level. This kind of statements prevailing with mental patients, the conversation between observer and subject tends to the monologue.(4) Here we can find too that statements of a purely subjective nature appear as indicative ones. Even physical and logical terms applied by the subject during the sittings do not have any physical or logical reference. This characteristic of the subject often baffles the observer. So confusion of verbal levels occurs frequently.(5) The introduction of a psychological term like verstehen does not solve the problem under consideration, but renders the mystery only the better camouflaged.     

On Ultrafilter Logic and Special Functions

Logics for generally were introduced for handling assertions with vague notions,such as generally, most, several, etc., by generalized quantifiers, ultrafilter logic being an interesting case. Here, we show that ultrafilter logic can be faithfully embedded into a first-order theory of certain functions, called coherent. We also use generic functions (akin to Skolem functions) to enable elimination of the generalized quantifier. These devices permit using methods for classical first-order logic to reason about consequence in ultrafilter logic.Presented by André Fuhrmann     

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.     

On a certain class ofm-address machines

Conclusion It follows from the proved theorems that ifM =Q, (whereQ={0,q ₁,q ₂,...,q }) is a machine of the classM _F then there exist machinesM _i such thatM _i(1,c)=M (q _i,c) andQ _i={0, 1, 2, ..., +1} (i=1, 2, ..., ).And thus, if the way in which to an initial function of content of memorycC a machine assigns a final onecC is regarded as the only essential property of the machine then we can deal with the machines of the formM ={0, 1, 2, ..., }, and processes (t) (wheret=1,c,cC) only.Such approach can simplify the problem of defining particular machines of the classM _F , composing and simplifying them.Allatum est die 19 Januarii 1970     

From I: A/M to “Who am I?”—Aggregation/Massification and Trauma-Based Affects and Object Relations in Groups: A Response to Earl Hopper

Hopper's portrayal of the fourth basic assumption of Incohesion: Aggregation/Massification has two components: (1) a revision of Turquet's theory of BA Oneness to incorporate the polarity of aggregation and massification stemming from annihilation anxiety; and (2) a conception of the difficult patient as having an encapsulated psychosis. Hopper's theory of the encapsulated psychosis offers an important but incomplete perspective in explaining borderline and narcissistic pathology, as well as psychological trauma. In this response to Hopper, I suggest that the fourth assumption is in fact a still more primitive state of boundary opening and closing. I also see a need to differentiate trauma as such from borderline pathology, and further hold that the relationship between Hopper's British Independent theory and trauma theories based on dissociation needs to be clarified.     

Job burnout and job leaving in public school teachers: Implications for stress management

This study addressed the questions of whether selected teacher and organizational variables contributed to (a) significant amounts of variance in teachers' scores on three components of burnout, and (b) teachers' intentions to leave special education teaching. Study participants (N =490) included a sample of respondents to a survey of all of the 1096 special education teachers in Hawaii. Instruments used in this study included the Maslach Burnout Inventory, the Porter Need Satisfaction Questionnaire, and the Special Education Teacher Survey. Results of multiple regression analyses indicated that for the burnout components, Emotional Exhaustion and Depersonalization, relatively large and significant amounts of variance could be accounted for by a set of predictor variables. For the third burnout component, Personal Accomplishment, the variance accounted for by a set of predictor variables was significant but small. Stepwise discriminant function analysis was used to distinguish between teachers who stated they did or did not intend to leave special education teaching. Eight variables were identified as predictors of Intention to leave special education teaching, correctly classifying 73% of teachers into the appropriate Yes-Leaving and No-Leaving groups.This research was conducted in partial fulfillment of requirements for the Doctoral dissertation by the first author.     

A further analysis of the affective meanings associated with male and female sex-trait stereotypes

This study was concerned with the qualitative differences in the male and female sex-trait stereotypes. Previous research employing the item pool of the Adjective Check List (ACL) had indicated no relationship between the stereotype loading of the adjectives and their favorability ratings. In the present study, university students rated the ACL items for strength and activity, and these ratings were used to demonstrate that the male stereotype was appreciably stronger and more active than the female stereotype. It was found that the strength ratings were highly correlated with both activity and favorability ratings which were, themselves, unrelated. It was concluded that the principal qualitative difference between the stereotypes lay in the connotations of activity and passivity associated, respectively, with the male and female stereotype traits, and that any assertion of greater social desirability for the male stereotype was based on its greater activity and not, as is often supposed, on its greater favorability.     

O pojęciu zdania analitycznego

Rezultaty przedstawione w pracy niniejszej pokrywaj si czciowo z wynikami osignitymi przezR. Wójcickiego w pracy:Analityczne komponenty definicji arbitralnych. Studia Logica, t. XIV. Dotyczy to gównie rezultatów zawartych w czci pierwszej. Chciabym podkreli, i wyniki R. Wójcickiego uzyskane zostay cakowicie niezalenie od rezultatów przedstawionych w pracy obecnej.Allatum est die 16 Aprilis 1962     

On superintuitionistic logics as fragments of proof logic extensions

Coming fromI andCl, i.e. from intuitionistic and classical propositional calculi with the substitution rule postulated, and using the sign to add a new connective there have been considered here: Grzegorozyk's logicGrz, the proof logicG and the proof-intuitionistic logicI set up correspondingly by the calculiFor any calculus we denote by the set of all formulae of the calculus and by the lattice of all logics that are the extensions of the logic of the calculus, i.e. sets of formulae containing the axioms of and closed with respect to its rules of inference. In the logiclG the sign is decoded as follows: A = (A & A). The result of placing in the formulaA before each of its subformula is denoted byTrA. The maps are defined (in the definitions of x and the decoding of is meant), by virtue of which the diagram is constructedIn this diagram the maps, x and are isomorphisms, thereforex ^–1 = ; and the maps and are the semilattice epimorphisms that are not commutative with lattice operation +. Besides, the given diagram is commutative, and the next equalities take place: ^–1 = ^–1 and = ^–1 x. The latter implies in particular that any superintuitionistic logic is a superintuitionistic fragment of some proof logic extension.     

Distance and fusion in Robinson Jeffers' “the purse-seine” and other poems

Distance and fusion are fundamental ideas in Bowenian thinking, especially as expressed in the dynamic of distancing and pursuing. In this paper I have used these ideas as a means to briefly examine a short selection of Robinson Jeffers' poetry, which provides us with a literary example of these concepts in action.My thanks to M. K. Lane and the anonymous reviewers of an earlier draft of this article for their many suggestions, especially to the reviewer who helped me better distinguish between distance and fusion, and intimacy and autonomy.     

Six-year-old children's understanding of sentences adjoined with time adverbs

The adjoining of clauses with temporal links is the basis for many sentences that convey sequence of events. The present study attempts to delineate 6-year-old children's (N=30) understanding of the meaning sequences imparted by sentences adjoined with after, before, and until. Their performance of the meaning sequence for each of 24 carefully constructed sentences is compared to an adult model. Analysis of the results (using a Wilcoxon Matched Pairs Signed Rank Test) indicated that: (1)Ss understood sentences adjoined with after according to an adult model more frequently than before adjoined sentences (P<0.01); (b) Until adjoined sentences with a negative marker in the main clause were understood according to an adult model more often than until adjoined sentences with no such negative element, but the difference was not significant at a=0.01; (3)Ss understood before adjoined sentences according to an adult model more often than until adjoined sentences, but the difference was not significant at a=0.01. In general, the results indicated that 6-year-olds have not yet completed development of an adult grammar with respect to adjoining clauses with temporal links, after, before, and until.     

The Origin of the Concept of “Allgemeinbildung” in 18th Century Germany

The German theory of education refers mainly to what is called Bildung. The historical sense of Bildung is not cultivaion, but cultivation for inwardness. This concept has two sources, the neo-platonic inner soul on one hand, pietistic piety on the other hand. The article shows that these sources had been part of European discussions before the development of national cultures after 1750. So the German concept of Bildung, famous for the German Sonderweg in culture and politics, had been composed out of non-German sources. The nationalizaiton of inwardness began at the end of the 18th century and was established in 19th century German Higher Education.     

Action incompleteness

The author has previously introduced an operator into dynamic logic which takes formulae to terms; the suggested reading of A was the bringing about of A or the seeing to it that A. After criticism from S. K. Thomason and T. J. Surendonk the author now presents an improved version of his theory. The crucial feature is the introduction of an operatorOK taking terms to formulae; the suggested reading of OK is always terminates.     

Lexical insertion,inflection, and derivation: Creative processes in word production

This study examines the distinction between creative and noncreative behavior as applied to the production of words and sentences. Under one hypothesis words such as governor and government are stored as independent units and produced by rote, but under another these nouns are not produced as fully integrated units but are generated by rules for combining stems (govern) and affixes (-ment and -or). Analyses of German and English speech errors supported the generation-by-rule thesis and indicated that word stems, prefixes, and suffixes must be separately stored in the internal lexicon and marked as to syntactic function in combining with other word components. The data also suggested a three-stage model of lexical processes in the production of speech: a lexical insertion stage whereby abstract lexical formatives are called on or introduced into sentences by means of abstract syntactic and semantic features; a rule application stage whereby feature agreement rules are applied to the formative and then inflectional, derivational, and phonological rules are applied to derive the phonetic string; finally a serial output stage whereby the phonetic string is translated into serially ordered motor commands.This research was supported by NIMH Grant RO 19964 to Donald Mackay.     

Death and the “life review” in Halakhah

Coping with old age involves resolving the task of integrity versus despair, which demands a nondefensive confrontation with the inevitability of death. Halakhah (Jewish ethics) also considered this task critical in later years of life, spoke of death's inevitability, and attempted to discourage denial of death. The Jewish approach seems compatible with Butler's concept of life review as a reconciliation with death and a reintegration of one's identity that occurs throughout later years. While the Eriksonian goal is confronting old age with a certain capacity for wisdom, the rabbis maintained that such wisdom must culminate in the creative act of repentance.     

Moral Responsibility, Determinism, and the Ability to do Otherwise

In his classic paper, The Principle of Alternate Possibilities, Harry Frankfurt presented counterexamples to the principle named in his title: A person is morally responsible for what he has done only if he could have done otherwise. He went on to argue that the falsity of the Principle of Alternate Possibilities (PAP) implied that the debate between the compatibilists and the incompatibilists (as regards determinism and the ability to do otherwise) did not have the significance that both parties had attributed to it -- since moral responsibility could exist even if no one was able to do otherwise. I have argued that even if PAP is false, there are other principles that imply that moral responsibility entails the ability to do otherwise, and that these principles are immune to Frankfurt-style counterexamples. Frankfurt has attempted to show that my arguments for this conclusion fail. This paper is a rejoinder to that reply; I argue that he has failed to show this.     

Making noises in counterpoint or chorus: Putnam''s rejection of relativism

Putnam's internal realism entails the simultaneous rejection of metaphysical realism and (anything goes or total or cultural) relativism. Putnam argues, in some places, that relativism is self-contradictory, and in others, that it is self-refuting. This paper attempts the exegetical task of explicating these challenging arguments, and the critical task of suggesting that a full-blown epistemological relativism may be capable of surviving the Putnam attack.