Let Λ denote the semiring of isols. We characterize existential completeness for Nerode subsemirings of Λ, by means of a purely isol-theoretic “Σ1 separation property”. Our characterization is purely isol-theoretic in that it is formulated entirely in terms of the extensions to Λ of the Σ1 subsets of the natural numbers. Advantage is taken of a special kind of isol first conjectured to exist by Ellentuck and first proven to exist by Barback . In addition, we strengthen the negative part (...) of [13] by showing that existential completeness is not secured, for a given Nerode semiring, by either a certain “functional closure” property for the extensions of partial recursive functions or the property of “pulling in” some portion of each partial recursive fiber; these latter results are perhaps a little surprising. (shrink)

Let T be a complete first-order theory over a finite relational language which is axiomatized by universal and existential sentences. It is shown that T is almost trivial in the sense that the universe of any model of T can be written $F \overset{\cdot}{\cup} I_1 \overset{\cdot}{\cup} I_2 \overset{\cdot}{\cup} \cdots \overset{\cdot}{\cup} I_n$ , where F is finite and I 1 , I 2 ,...,I n are mutually indiscernible over F. Some results about complete theories with ∃∀-axioms over a finite (...) relational language are also mentioned. (shrink)

We use the spaces T n and E n of complete types and of existential types to investigate various notions which appear in the theory of the algebraic structure of models.

Peirce’s diagrammatic system of Existential Graphs (EGα)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$EG_{\alpha })$$\end{document} is a logical proof system corresponding to the Propositional Calculus (PL). Most known proofs of soundness and completeness for EGα\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$EG_{\alpha }$$\end{document} depend upon a translation of Peirce’s diagrammatic syntax into that of a suitable Frege-style system. In this paper, drawing upon standard results but using the native diagrammatic notational framework of the graphs, we present (...) a purely syntactic proof of soundness, and hence consistency, for EGα\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$EG_{\alpha }$$\end{document}, along with two separate completeness proofs that are constructive in the sense that we provide an algorithm in each case to construct an EGα\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$EG_{\alpha }$$\end{document} formal proof starting from the empty Sheet of Assertion, given any expression that is in fact a tautology according to the standard semantics of the system. (shrink)

We construct a recursive ultrapower F/U such that F/U is a tame 1-model in the sense of [6, §3] and FU is existentially incomplete in the models of II2 arithmetic. This enables us to answer in the negative a question about closure with respect to recursive fibers of certain special semirings Γ of isols termed tame models by Barback. Erik Ellentuck had conjuctured that all such semirings enjoy the closure property in question. Our result is that while many do, (...) some do not. (shrink)

Bu çalışmanın amacı, Thomas Bernhard’ın romanlarında yaşam, ölüm ve intihar üçgeninde insanın varoluşsal çabasını varoluşçuluk öğretisi ekseninde anlamaktır. Bu amaç doğrultusunda Bernhard’ın Bitik Adam ve Düzelti romanlarındaki intihar edimi, ana karakterler merkezinde tematik analiz ile çözümlenmeye çalışılmıştır. Anlamsız dünyada çetin bir varoluş imtihanından geçen insanın seçeneğine odaklanan Bernhard, insanın kendi varoluşu için dünyanın sonsuz uyumsuzluğunun gerekli olduğunu kabul etmesi gerektiğini savunur. Bu kabul, insanın pasifize olmasını değil biteviye başkaldırarak varoluşun alternatif imkânlarını temsil etmektedir. Çalışmanın sonucunda, romanlarda karakterleri intihara götüren temel (...) faktörler; insanın var olma çabasında koşul ve zamanların belirlenimciliği ile özgürlüğün iç içe oluşunu kavrayamamak, istem ve tasarımlarında kusursuzluk idealini aşamamak, durumlara gösterilen başkaldırıyı sürdürememek, yinelenen varoluş seçeneklerini değerlendirememektir. Bu suretle yaşam kapanına sıkışan insan, iradesine bahşedilen tek ve en özgür edimi olarak intiharı seçecek ancak yok olan beden gerçeğine karşılık yaşam var olmaya devam edecektir. (shrink)

The notion of existential catastrophe is increasingly appealed to in discussion of risk management around emerging technologies, but it is not completely clear what this notion amounts to. Here, I provide an opinionated survey of the space of plausibly useful definitions of existential catastrophe. Inter alia, I discuss: whether to define existential catastrophe in ex post or ex ante terms, whether an ex ante definition should be in terms of loss of expected value or loss of potential, and what kind (...) of probabilities should be involved in any appeal to expected value. (shrink)

Several countries have legalized euthanasia on the basis of medically diagnosable suffering over the last decennial; the criteria to which they adhere differ. The topic of this article is euthanasia on the basis of existential suffering. This article presents a recent proposal to legalize euthanasia for people who experience such suffering and then discusses the issue of what the value of life may be, and whether the standard that life is normally something positive should be accepted. This provides the foundation (...) to answer the question of whether euthanasia on the basis of existential suffering should be allowed. (shrink)

The class of all Artinian local rings of length at most l is ∀ 2 -elementary, axiomatised by a finite set of axioms Art l . We show that its existentially closed models are Gorenstein, of length exactly l and their residue fields are algebraically closed, and, conversely, every existentially closed model is of this form. The theory Got l of all Artinian local Gorenstein rings of length l with algebraically closed residue field is model complete and (...) the theory Art l is companionable, with model-companion Got l. (shrink)

We characterize when the elementary diagram of a mutually algebraic structure has a model complete theory, and give an explicit description of a set of existential formulas to which every formula is equivalent. This characterization yields a new, more constructive proof that the elementary diagram of any model of a strongly minimal, trivial theory is model complete.

Martin Heidegger’s existential account of care in _Being and Time_ (2010) provides us with an opportunity to reimagine what the proper theoretical grounding of an ethic of care might be. Heidegger’s account of care serves to deconstruct the two primary foundations that an ethic of care is often based upon. Namely, that we are inevitably interdependent upon one another and/or possess an innate disposition to care for fellow humans in need. Heidegger’s account reveals that both positions are founded upon an (...) ontic (meaning factual existence), as opposed to an ontological (which refers to the nature of being), understanding of care. The distinctions between an ontic and ontological understanding of care are significant. Yet, I maintain that they are not completely incompatible. Both Heidegger and care ethicists contend that our existence with others is understood through a relational ontology. Furthermore, there are certain ontological structures from Heidegger which resonate with an ethic of care. Two key existential structures are leaping-ahead and being-guilty. These existential structures are latent in care ethics, and by explicitly revealing them I reinforce the connection between Heidegger’s account and care theory. Lastly, I develop the theoretical foundations of care ethics by proposing an existential ethic of care. (shrink)

We construct an existentially undecidable complete discretely valued field of mixed characteristic with existentially decidable residue field and decidable algebraic part, answering a question by Anscombe–Fehm in a strong way. Along the way, we construct an existentially decidable field of positive characteristic with an existentially undecidable finite extension, modifying a construction due to Kesavan Thanagopal.

We give a new and elementary construction of primitive positive decomposition of higher arity relations into binary relations on finite domains. Such decompositions come up in applications to constraint satisfaction problems, clone theory and relational databases. The construction exploits functional completeness of 2-input functions in many-valued logic by interpreting relations as graphs of partially defined multivalued ‘functions’. The ‘functions’ are then composed from ordinary functions in the usual sense. The construction is computationally effective and relies on well-developed methods of functional (...) decomposition, but reduces relations only to ternary relations. An additional construction then decomposes ternary into binary relations, also effectively, by converting certain disjunctions into existential quantifications. The result gives a uniform proof of Peirce’s reduction thesis on finite domains, and shows that the graph of any Sheffer function composes all relations there. (shrink)

We introduce the notion of positive strong amalgamation property and we investigate some universal forms and properties of this notion. Considering the close relationship between the amalgamation property and the notion of complete theories, we explore the fundamental properties of positively complete theories, and we illustrate the behaviour of this notion by bringing changes to the language of the theory through the groups theory.

Despite their growing popularity, little is known about the psychological effects of participating in past-life meditation groups in contemporary western contexts. We conducted a study to re-create some of the conditions observed in the field by facilitating a group of adults interested in exploring past life meditation. Before the session, participants completed a survey about their afterlife beliefs and associated experiences. Participants also completed questionnaires measuring meaningfulness in life and fear of death before and after the session. In the sample (...) (n = 125), just over half of the participants (52%) reported having a past life memory or vision during the session. Higher paranormal beliefs predicted reporting a past life memory or vision. We also found that having prior memories or visions of having lived before, but not the general belief in having a past life, predicted reporting having past life experiences during the session. Consistent with our predictions, participants who reported having a past life memory or vision also reported reduced existential death distress and increased meaningfulness in life following the session, compared to those who did not report these experiences. (shrink)

El psicoanálisis existencial es una de esas críticas constructivas derivadas del psicoanálisis empírico que intenta abrirse camino como alternativa, renovación y modelo de terapia psicoanalítica. Ha encontrado una fundamentación óntico-ontológica desde la cual mostrar al ser descrito tal como se manifiesta en tres estadios concretos: el para-sí, en-sí y para-otro, para llegar a ver que las relaciones con los otros son las que nos provocan esos desequilibrios psíquicos. Nuestro psicoanálisis se plantea como una superación al psicoanálisis empírico en el rechazo (...) al postulado del inconsciente y en la elección que renuncia a suponer una acción mecánica del medio sobre el sujeto considerado a abandonar la simbología utilizada hasta entonces. El psicoanálisis existencial deberá ser enteramente flexible y amoldable a los menores cambios observables en el sujeto, ya que se trata de descubrir una elección no un estado. Como el psicoanálisis existencial tiene como objeto descubrir una elección, deberá tener siempre presente que su objeto no es algo hundido en las tinieblas del inconsciente, sino una determinación consciente y libre. Finalmente, la propuesta es una terapia psicoanalítica ya que la persona es una constante proyección en el mundo, el método existencial, se orienta desde el principio hacia una comprensión del ser y no debe asignarse otro objetivo que encontrar el ser y la manera de ser del ser frente a ese ser.Existential Psychoanalysis is one of the most constructive critics based on empirical psychoanalysis which attempts to open up new paths as an alternative, renovation and model of psychoanalytical therapy. An ontic-ontological foundation has been discovered from which it can be described in 3 different concrete states: for someone, in someone or for someone else, to be able to see that our relationships with others are those which cause psychic unbalance. Our psychoanalysis overcomes empirical psychoanalysis in rejection to postulate from the unconscious and in the election which renounces to suppose a mechanical action from the medium on the subject considered to abandon the symbology used until then. Existential psychoanalysis should be completely flexible and changeable to the minor changes which can be observed in the subject, now that it is a case of discovering an election not a state. Due to the fact that the psychoanalysis has as objective to discover an election, it should always have present that its objective is not something united in the darkness of the unconscious, but more of a conscious and free determination. Lastly, the proposition is a psychoanalytical therapy now that the person is a constant projection in the world, the existential method, which is oriented from the beginning towards an understanding of the being and another objective should not be assigned other than find ways of being and the way of being against that being. (shrink)

Since the publication of The verb “be” in Ancient Greek by Charles Kahn, people have put a lot of emphasis and invested too much labor in all kinds of historico-philological analyses in order to resolve philosophical questions regarding the concept of existence in Greek thought. Useful as these analyses might be, they cannot provide us with conclusive answers to the specific philosophical questions under scrutiny, and, perhaps, it is time for us to abandon the overwhelming optimist motivating the pioneers behind (...) these attempts. I use the Sophist as a case study. I conclude that whether the Form of Being represents existence or predication cannot be settled on speculation regarding the syntax of the verb εἶναι; absolute εἶναι need not be existential in meaning, and complemented εἶναι may be existential in meaning. (shrink)

In this paper I aim to examine Heidegger’s analysis of existential spatiality in Being and Time in the light of Sloterdijk’s criticism of it. Sloterdijk states in Spheres I that Heidegger presented, in Being and Time, an “embryonically revolutionary” approach to being and space but did not complete it. His own ‘Spheres Project’ would purport fill this gap. Based on the analysis of the fundamental moments of existential spatiality (§§12 to 28 and §70 of Being and Time), and taking (...) into account comments made by Heidegger himself in later years, I will attempt to answer the question of the alleged unfinished character of the analysis of existential spatiality in Being and Time. (shrink)

Purpose. Aging is intricate process of self-transformation in view of involution of body, loss of sexual attractiveness, but at the same time, old age is a time for reconsideration of self-existence in time and in the world within coherence of life sense targets and their realization. Unique individual experience of growing old implemented in Ukrainian literature can complete the data received by gerontology. Moreover gender approach in literary gerontology highlights masculine / feminine phenotypical features of internal reverberating of aging. (...) Theoretical basis. To inquire into existential and psychological problems of aging exemplified in the twentieth-century Ukrainian Lyrics it is seems to be the most effective to employ philosophical and psychological approaches in gerontology, as well as feministic studies on elder female body discrimination, in particular in literature. Originality. This research paves the way to the development of gender and literary dimensions in Ukrainian gerontology and anthropology in general. Some of the existential and psychological problems of aging are revealed on the material of 20th-century Ukrainian poetry. The individual lyric experience of aging in different gender moods is anchored mostly in psychic, mental, sense-life strategies. Conclusions. Among the feminine strategies of aging self-reception there are observation of own elder body with anxiety and fear, its "invisibility", deepened feelings of loneliness, self-estrangement, but also finding the sense of life and soul harmony in own family, offspring. Masculine self-reception of aging deals with ideal spiritual model of Wise old man – more abstract than personal; masculine anxiety is caused by physical bodily declining, not attractiveness, but strength and power loosing. (shrink)

The purpose of this paper is to clarify the relationship between various conditions implying essential undecidability: our main result is that there exists a theory T in which all partially recursive functions are representable, yet T does not interpret Robinson’s theory R. To this end, we borrow tools from model theory — specifically, we investigate model-theoretic properties of the model completion of the empty theory in a language with function symbols. We obtain a certain characterization of ∃∀ theories interpretable in (...) existential theories in the process. (shrink)

In this paper an alternative Skolemization method is introduced that, for a large class of formulas, is sound and complete with respect to intuitionistic logic. This class extends the class of formulas for which standard Skolemization is sound and complete and includes all formulas in which all strong quantifiers are existential. The method makes use of an existence predicate first introduced by Dana Scott.

The variety of Brouwerian semilattices is amalgamable and locally finite; hence, by well-known results [19], it has a model completion. In this article, we supply a finite and rather simple axiomatization of the model completion.

The logics of the modal operators and of the quantifiers show striking analogies. The analogies are so extensive that, when a special class of entities (possible worlds) is postulated, natural and non-arbitrary translation procedures can be defined from the language with the modal operators into a purely quantificational one, under which the necessity and possibility operators translate into universal and existential quantifiers. In view of this I would be willing to classify the modal operators as ‘disguised’ quantifiers, and I think (...) that wholehearted acceptance of modal language should be considered to carry ontological commitment to something like possible worldsConsidered as two languages for describing the same subject matter, modal and purely quantificational languages show interesting differences. The operator variables of the purely quantificational languages give them more power than the modal languages, but at least some of the functions performed by the apparatus of operator variables are also performed, in a more primitive and less versatile way, by actuality operators in modal languages.A final note. Quine has written much on the inter-relations of quantifiers, identity, and the concept of existence. These, he holds, form a tightly knit conceptual system which has been evolved to a high point of perfection, but which might conceivably change yet further.29 He has also dropped hints about the possibility of a simpler, primitive or defective version of the system, in which the quantifiers are not backed up in their accustomed way by the concept of identity. He has dubbed the resulting concept a ‘pre-individuative’ concept of existence, or a concept of ‘entity without identity.’ What would a pre-individuative concept of existence be like? Quine has sometimes suggested that one might be embodied in the use of mass nouns, but the identity concept is used in connection with stuff as well as with things: “is that the same coffee that was in the cup last night?” I would submit that modality provides a better case. In view of the comparative weakness of modal languages, compared to the explicitly quantificational ones Quine takes as canonical, there is surely a sense in which the concept of existence embodied in that disguised existential quantifier, the possibility operator, is a defective one. And as we have seen, one of the differences between modal operators and explicit quantifiers is that modal operators cannot be joined with the identity predicate in the way quantifiers with operator variables can. Surely, then, there is a sense in which ordinary speech, as opposed to the metaphysical theorizing of a Leibniz or a David Lewis, conceives of possible worlds as entities without identity. (shrink)

Problems and questions originally raised by Robert Nozick in his famous thought experiment ‘The Experience Machine’ are frequently invoked in the current discourse concerning virtual worlds. Having conceptualized his Gedankenexperiment in the early seventies, Nozick could not fully anticipate the numerous and profound ways in which the diffusion of computer simulations and video games came to affect the Western world. -/- This article does not articulate whether or not the virtual worlds of video games, digital simulations, and virtual technologies currently (...) actualize (or will actualize) Nozick’s thought experiment. Instead, it proposes a philosophical reflection that focuses on human experiences in the upcoming age of their ‘technical reproducibility’. -/- In pursuing that objective, this article integrates and supplements some of the interrogatives proposed in Robert Nozick’s thought experiment. More specifically, through the lenses of existentialism and philosophy of technology, this article tackles the technical and cultural heritage of virtual reality, and unpacks its potential to function as a tool for self-discovery and self-construction. Ultimately, it provides an interpretation of virtual technologies as novel existential domains. Virtual worlds will not be understood as the contexts where human beings can find completion and satisfaction, but rather as instruments that enable us to embrace ourselves and negotiate with various aspects of our (individual as well as collective) existence in previously-unexperienced guises. (shrink)

`Hans Cohn has given us a personal and valuable statement about the theoretical underpinnings of his work as a psychotherapist. These can be little doubt about his contribution to our thinking practice is invaluable. Students will find Cohn's easygoing exposition of complex ideas enormously helpful' - Professor Emmy van Deurzen, Existential Analysis `One of the most important books published this year. This long-awaited book by the foremost expert on the relationship between Heidegger and psychotherapy, manages to encapsulate the essence of (...) Heidegger's thinking and make of understandable and relevant to therapists without losing any of the original meaning' - Counsellingbooks.com Anyone interested in modern philosophy is familiar with the name of Martin Heidegger but there is a serious gap in even the most complete accounts of his life and thought. This is Heidegger's association with, and influence on, psychotherapy. Hans C Cohn explores the role of Heidegger's thought in providing an alternative basis for psychotherapeutic practice to the dominant psychodynamic, humanistic and cognitive approaches, also focusing strongly on the practical therapeutic relevance of Heidegger's ideas. This book will be essential reading for students and teachers of modern philosophy, as well as existential psychotherapists, and all practitioners interested in existential approaches to therapy. (shrink)

Being a substitute in sport appears to contradict the rationale behind being involved in that sport, especially in those sports whereby substitutes frequently remain unused or are brought on to the field of play for the final moments of that game. For the coach or manager, substitutes function as a way to improve the team achieving a particular end, namely to win the game; whether to replace an injured or tired player, to change a team’s structure or tactics, to (...) class='Hi'>complete a specialised manoeuvre (such as goal kicking in American football or a short corner in hockey), or to run down the clock. Whether a substitute is afforded an opportunity of playing the game appears to be directed by others; arguably if one had a choice in the matter one would chose to be on the field of play rather than off it. Nevertheless, the Existentialist position is that our situation is always inexorably one that is freely chosen. To argue that one has not freely chosen one’s position is to be ‘inauthentic’. Furthermore, to conceptualise one’s manifestation and to be treated by others as a thing ‘in-itself’ – such as a substitute - is to fall into ‘bad faith’. Culbertson (1) has already argued that elite competitive sport is an arena which promotes rather than avoids bad faith due to its constituent factors. Culbertson’s frame of reference primarily applied to sporting events that involve individuals competing in co-active, parallel competition - such as athletics, swimming or weightlifting - whereby bad faith is generated via a tacit acceptance of ever improving and quantifiable performance. The purpose of this paper is a continuation of such an enquiry but with a redirection of focus away from parallel competition byindividuals, towards team competitions which are, by nature, less concerned with an unremitting contest against time, distance or some other measurable concept. This paper sets out to examine the nature of the substitute in sport, who appears to be equally liable to find herself being ‘inauthentic’ and/or in ‘bad-faith’. It attempts to consider the nature of these concepts and offer direction as to how substitutes can attempt to realize the Existential ideal. (shrink)

Syllogistics reduces to only two rules of inference: monotonicity and symmetry, plus a third if one wants to take existential import into account. We give an implementation that uses only the monotonicity and symmetry rules, with an addendum for the treatment of existential import. Soundness follows from the monotonicity properties and symmetry properties of the Aristotelean quantifiers, while completeness for syllogistic theory is proved by direct inspection of the valid syllogisms. Next, the valid syllogisms are decomposed in terms of the (...) rules they involve. The implementation uses Haskell [8], and is given in ‘literate programming’ style [9]. (shrink)

This paper investigates a problem related to quantifiers which has some analogies to that of propositional completeness I give a definition of quantifier in many-valued logics generalizing the cases which already occur in first order many- valued logics. Though other definitions are possible, this particular one, which I call distribution quantifiers, generalizes the classical quantifiers in a very natural way, and occurs in finite numbers in every m-valued logic. We then call the problem of quantificationa2 completeness in m-valued logic the (...) problem of characterizing which are the quantifiers in a given language which can generate all other quantifiers in this language, using the connectives, as is the case, for example, of the universal and exis- tential quantifiers in classical logic, using negation. We are interested, in particular, in those many-valued quantifiers which closely mimic the behavior of existential an universal quantifiers in generating all other quantifiers using negation: these I call perfect quantifiers, as defined below. The main result of this paper is the characterization of all perfect quantifiers in 3-valued logics, which are complete if the logic is functionally complete. As a byproduct, we obtain the same result for the classical logic, which we include mainly for motivation. (shrink)

For a ring R, Hilbert’s Tenth Problem $HTP$ is the set of polynomial equations over R, in several variables, with solutions in R. We view $HTP$ as an enumeration operator, mapping each set W of prime numbers to $HTP$, which is naturally viewed as a set of polynomials in $\mathbb {Z}[X_1,X_2,\ldots ]$. It is known that for almost all W, the jump $W'$ does not $1$ -reduce to $HTP$. In contrast, we show that every Turing degree contains a set W (...) for which such a $1$ -reduction does hold: these W are said to be HTP-complete. Continuing, we derive additional results regarding the impossibility that a decision procedure for $W'$ from $HTP$ can succeed uniformly on a set of measure $1$, and regarding the consequences for the boundary sets of the $HTP$ operator in case $\mathbb {Z}$ has an existential definition in $\mathbb {Q}$. (shrink)

This paper provides a phenomenology of the suicidal process. It begins with an examination of the self and the breaks that occur within the world that the suicidal individual endures. This includes an examination of suicidal hopelessness, termed in this paper as ontological petrification. It follows with the role in which hope plays in the suicidal. The paper then turns to carrying out the action of suicide, including a discussion of the suicide note and the developing form of the suicide (...) note as found in live-streams on social media. The paper concludes by describing the completion of the suicidal process, and the persistence of the suicidal drive in the suicidal individual. The paper makes use of suicide notes, video suicide notes, and stories of suicides. (shrink)

Usually in logic, proof systems are defined having in mind proving properties like validity and semantic consequence. It seems worthwhile to address the problem of having proof systems where satisfiability is a primitive notion in the sense that a formal derivation means that a finite set of formulas is satisfiable. Moreover, it would be useful to cover within the same framework as many logics as possible. We consider Kripke semantics where the properties of the constructors are provided by valuation constraints (...) as the common ground of those logics. This includes for instance intuitionistic logic, paraconsistent Nelson’s logic ${\textsf{N4}}$, paraconsistent logic ${\textsf{imbC}}$ and modal logics among others. After specifying a logic by those valuation constraints, we show how to induce automatically and from scratch an existential proof system for that logic. The rules of the proof system are shown to be invertible. General results of soundness and completeness are proved and then applied to the logics at hand. (shrink)

In 2015 Dag Prawitz proposed an Ecumenical system where classical and intuitionistic logic could coexist in peace. The classical logician and the intuitionistic logician would share the universal quantifier, conjunction, negation and the constant for the absurd, but they would each have their own existential quantifier, disjunction and implication, with different meanings. Prawitz’ main idea is that these different meanings are given by a semantical framework that can be accepted by both parties. The aim of the present paper is [1] (...) to prove the normalization theorem for the propositional fragment NEp of Prawitz’ ecumenical system, and [2] to show that NEp is sound and complete with respect to a Kripke-style semantics for the language of NEp. (shrink)

In this paper we give a differential lifting principle which provides a general method to geometrically axiomatize the model companion (if it exists) of some theories of differential topological fields. The topological fields we consider here are in fact topological systems in the sense of van den Dries, and the lifting principle we develop is a generalization of the geometric axiomatization of the theory DCF₀ given by Pierce and Pillay. Moreover, it provides a geometric alternative to the axiomatizations obtained by (...) Tressl and Guzy/Point in separate papers where the authors also build general schemes of axioms for some model complete theories of differential fields. We first characterize the existentially closed models of a given theory of differential topological fields and then, under an additional hypothesis of largeness, we show how to modify this characterization to get a general scheme of first-order axioms for the model companion of any large theory of differential topological fields. We conclude with an application of this lifting principle proving that, in existentially closed models of a large theory of differential topological fields, the jet-spaces are dense in their ambient topological space. (shrink)

In a previous work we introduced the algorithm \SQEMA\ for computing first-order equivalents and proving canonicity of modal formulae, and thus established a very general correspondence and canonical completeness result. \SQEMA\ is based on transformation rules, the most important of which employs a modal version of a result by Ackermann that enables elimination of an existentially quantified predicate variable in a formula, provided a certain negative polarity condition on that variable is satisfied. In this paper we develop several extensions (...) of \SQEMA\ where that syntactic condition is replaced by a semantic one, viz. downward monotonicity. For the first, and most general, extension \SSQEMA\ we prove correctness for a large class of modal formulae containing an extension of the Sahlqvist formulae, defined by replacing polarity with monotonicity. By employing a special modal version of Lyndon's monotonicity theorem and imposing additional requirements on the Ackermann rule we obtain restricted versions of \SSQEMA\ which guarantee canonicity, too. (shrink)

We consider the structure of all labeled trees, called also infinite terms, in the first order language with function symbols in a recursive signature of cardinality at least two and at least a symbol of arity two, with equality and a binary relation symbol which is interpreted to be the subtree relation. The existential theory over of this structure is decidable (see Tulipani [9]), but more complex fragments of the theory are undecidable. We prove that the theory of the structure (...) is in , where formulas are those in prenex form consisting of a string of unbounded existential quantifiers followed by a string of arbitrary quantifiers all bounded with respect to . Since the fragment of the theory was already known to be -hard (see Marongiu and Tulipani [5]), it is now established to be -complete. (shrink)

The paper presents a compositional approach to the verification of CTL* properties over reactive systems. Both symbolic model-checking and deductive verification are considered. Both methods are based on two decomposition principles. A general state formula is decomposed into basic state formulas which are CTL* formulas with no embedded path quantifiers. To deal with arbitrary basic state formulas, we introduce another reduction principle which replaces each basic path formula, i.e., path formulas whose principal operator is temporal and which contain no embedded (...) temporal operators or path quantifiers, by a newly introduced boolean variable which is added to the system. Thus, both the algorithmic and the deductive methods are based on two statification transformations which successively replace temporal formulas by assertions which contain no path quantifiers or temporal operators. Performing these decompositions repeatedly, we remain with basic assertional formulas, i.e., formulas of the form Efp and Afp for some assertion p. In the model-checking method we present a single symbolic algorithm to verify both universal and existential basic assertional properties. In the deductive method we present a small set of proof rules and show that this set is sound and relatively complete for verifying universal and existential basic assertional properties over reactive systems. Together with two proof rules for the decompositions, we obtain a sound and relatively complete proof system for arbitrary CTL* properties. Interestingly, the deductive approach for CTL* presented here, offers a viable new approach to the deductive verification of arbitrary LTL formulas. The paper corrects a previous preliminary version of a deductive system for CTL*, in which some of the rules were unsound. The correction is based on the introduction of a new type of temporal testers which are guaranteed to be non blocking. That is, when composed with a deadlock-free system, which is a key operation in the verification process, the resulting composed system is guaranteed to remain deadlock free. (shrink)

In the introduction, the problem of interpreting memory as the basic category of human existential experience was taken up. The history of philosophical analysis of that category was outlined. Having put forward the definitions, the basic types of memory, appearing in philosophical discourse, were presented. The relation taking place between memory and oblivion was adopted as the basic one for the analysis. The problem of symmetry in the memory – oblivion relation was reflected upon. The existential nature of experiencing memory (...) was indicated. The second part of the text was dedicated to the analysis of functioning of memory/oblivion phenomenon. That part included the discussion on the memory – oblivion relation as one of the most fundamental oppositions forming human identity. The meaning of the memory – oblivion relation for philosophy on the example of the phenomenon of writing was presented. In the consecutive part, the measurability of memorizing and forgetting processes was indicated. The text was completed by comments on axiology of memorizing and forgetting processes. (shrink)

The total ideology of the revolutionary-political themes of Ukrainian consciousness of the twentieth century, the poetization of the absurdly inverted hierarchy of values, was opposed by the new generation of artists with their philosophical and ethical orientation of their creativity. As I.Franko notes, they "... sought a completely modern European way to portray the peculiarity of the life of the Ukrainian people," revealing the unique collisionality of human existence, the diversity of psychological types, ideological orientations, and the human experience of (...) its existence on the background of this difficult time. However, Ukrainian writersphilosophers who talently laid the foundations of national culture, but are now returning to the generations of the Shattered Renaissance, filling black and bloody spots of troubled history of Ukraine. Among them are V. Pidmogylny, B. Antonovenko-Davidovich, G. Kosinka, D. Falkivsky, M.Ivchenko, T.Osmachka, E.Pluzhnik. This is a non-exhaustive list of the leading figures of the post-revolutionary period who were removed from the creative field, whose works are the golden fund of Ukrainian culture. (shrink)

We propose an original use of techniques from random graph theory to find a Monadic ∑ 1 1 sentence without an asymptotic probability. Our result implies that the 0-1 law fails for the logics ∑ 1 1 and ∑ 1 1 . Therefore we complete the classification of first-order prefix classes with or without equality, according to the existence of the 0-1 law for the corresponding ∑ 1 1 fragment. In addition, our counterexample can be viewed as a single (...) explanation of the failure of the 0-1 law of all the fragments of existential second-order logic for which the failure is already known. (shrink)

The article presents two gestures corresponding to two profound new understandings of Peirce's Continuum and Peirce's Existential Graphs. Vargas and Oostra have revolutionized Peirce's mathematical studies, thanks to a first complete model for Peirce's continuum provided by Vargas, and thanks to the emergence of intuitionistic existential graphs provided by Oostra. The article aims at showing how these careful mathematical constructions can be encrypted in very simple gestures.

Given a regular cardinal $\kappa $ such that $\kappa ^{<\kappa }=\kappa $, we study a class of toposes with enough points, the $\kappa $ -separable toposes. These are equivalent to sheaf toposes over a site with $\kappa $ -small limits that has at most $\kappa $ many objects and morphisms, the topology being generated by at most $\kappa $ many covering families, and that satisfy a further exactness property T. We prove that these toposes have enough $\kappa $ -points, that (...) is, points whose inverse image preserve all $\kappa $ -small limits. This generalizes the separable toposes of Makkai and Reyes, that are a particular case when $\kappa =\omega $, when property T is trivially satisfied. This result is essentially a completeness theorem for a certain infinitary logic that we call $\kappa $ -geometric, where conjunctions of less than $\kappa $ formulas and existential quantification on less than $\kappa $ many variables is allowed. We prove that $\kappa $ -geometric theories have a $\kappa $ -classifying topos having property T, the universal property being that models of the theory in a Grothendieck topos with property T correspond to $\kappa $ -geometric morphisms into that topos. Moreover, we prove that $\kappa $ -separable toposes occur as the $\kappa $ -classifying toposes of $\kappa $ -geometric theories of at most $\kappa $ many axioms in canonical form, and that every such $\kappa $ -classifying topos is $\kappa $ -separable. Finally, we consider the case when $\kappa $ is weakly compact and study the $\kappa $ -classifying topos of a $\kappa $ -coherent theory, that is, a theory where only disjunction of less than $\kappa $ formulas are allowed, obtaining a version of Deligne’s theorem for $\kappa $ -coherent toposes from which we can derive, among other things, Karp’s completeness theorem for infinitary classical logic. (shrink)

It is proved in this paper that the predicate logic of each complete constructive arithmetic theory T having the existential property is Π1T-complete. In this connection, the techniques of a uniform partial truth definition for intuitionistic arithmetic theories is used. The main theorem is applied to the characterization of the predicate logic corresponding to certain variant of the notion of realizable predicate formula. Namely, it is shown that the set of irrefutable predicate formulas is recursively isomorphic to the (...) complement of the set ︀. The notion of Σn-realizability is defined on the basis of the notion of Σn-function. It is proved that the predicate logic of Σn-realizability is Πω+1-hard. (shrink)

Russell’s use of incomplete symbols constituted progress in philosophy. They allowed Russell to make true negative existential claims, like ‘the present King of France does not exist’, and to analyse away logical constructs like tables. Russell’s view rested on the availability of complete symbols, logically proper names, which single out objects which we know by acquaintance, which we are committed to, and to whose existence discourse about apparent complexes can be reduced. Susan Stebbing enthusiastically embraced incomplete symbols for use (...) in negative existentials and in her innovative theory of metaphysical analysis. Yet she also raised trenchant objections to Russell’s assumption that complete symbols are purely referring expressions, equivalent to mere demonstration or pointing. Stebbing thought it could not be assumed that analysis terminates in objects of acquaintance. In this chapter I lay out Stebbing’s arguments and argue that they bear a striking similarity to those made by Stebbing’s former college’s Mistress, Constance Jones, whose influence on Russell is now largely forgotten but worth recovering. Jones defended a sense-reference (signification-denotation) distinction before Frege. Russell’s objections to that distinction in ‘On Denoting’ appear to borrow from Jones’s presentation of it. In Russell and Jones’s 1911 exchange at the Aristotelian Society, Jones’s arguments that names have signification and are more than mere noises or shapes, and that unless both signification and denotation are taken into account, all identity statements reduce to the trivial ‘a=a’ form, foreshadow Stebbing’s later arguments against complete symbols. (shrink)