The class \ of t rue p airing a lgebras is defined to be the class of relation algebras expanded with concrete set theoretical projection functions. The main results of the present paper is that neither the equational theory of \ nor the first order theory of \ are decidable. Moreover, we show that the set of all equations valid in \ is exactly on the \ level. We consider the class \ of the relation algebra reducts of \ ’s, (...) as well. We prove that the equational theory of \ is much simpler, namely, it is recursively enumerable. We also give motivation for our results and some connections to related work. (shrink)

In this paper we define computationally well-behaved versions of classical first-order logic and prove that the validity problem is decidable.

Henkin and Tarski proved that an atomic cylindric algebra in which every atom is a rectangle must be representable . This theorem and its analogues for quasi-polyadic algebras with and without equality are formulated in Henkin, Monk and Tarski [13]. We introduce a natural and more general notion of rectangular density that can be applied to arbitrary cylindric and quasi-polyadic algebras, not just atomic ones. We then show that every rectangularly dense cylindric algebra is representable, and we extend this result (...) to other classes of algebras of logic, for example quasi-polyadic algebras and substitution-cylindrification algebras with and without equality, relation algebras, and special Boolean monoids. The results of op. cit. mentioned above are special cases of our general theorems. We point out an error in the proof of the Henkin-Monk-Tarski representation theorem for atomic, equality-free, quasi-polyadic algebras with rectangular atoms. The error consists in the implicit assumption of a property that does not, in general, hold. We then give a correct proof of their theorem. Henkin and Tarski also introduced the notion of a rich cylindric algebra and proved in op. cit. that every rich cylindric algebra of finite dimension satisfying certain special identities is representable. We introduce a modification of the notion of a rich algebra that, in our opinion, renders it more natural. In particular, under this modification richness becomes a density notion. Moreover, our notion of richness applies not only to algebras with equality, such as cylindric algebras, but also to algebras without equality. We show that a finite dimensional algebra is rich iff it is rectangularly dense and quasi-atomic; moreover, each of these conditions is also equivalent to a very natural condition of point density . As a consequence, every finite dimensional rich algebra of logic is representable. We do not have to assume the validity of any special identities to establish this representability. Not only does this give an improvement of the Henkin-Tarski representation theorem for rich cylindric algebras, it solves positively an open problem in op. cit. concerning the representability of finite dimensional rich quasi-polyadic algebras without equality. (shrink)

We show that the equational theory of representable lattice-ordered residuated semigroups is not finitely axiomatizable. We apply this result to the problem of completeness of substructural logics.

We show that the equational theory of representable lower semilattice-ordered residuated semigroups is finitely based. We survey related results.

In this paper we show that relativized versions of relation set algebras and cylindric set algebras have undecidable equational theories if we include coordinatewise versions of the counting operations into the similarity type. We apply these results to the guarded fragment of first-order logic.

The class $$\mathsf{TPA}$$ TPA of t rue p airing a lgebras is defined to be the class of relation algebras expanded with concrete set theoretical projection functions. The main results of the present paper is that neither the equational theory of $$\mathsf{TPA}$$ TPA nor the first order theory of $$\mathsf{TPA}$$ TPA are decidable. Moreover, we show that the set of all equations valid in $$\mathsf{TPA}$$ TPA is exactly on the $$\Pi ^1_1$$ Π 1 1 level. We consider the class $$\mathsf{TPA}^-$$ (...) TPA - of the relation algebra reducts of $$\mathsf{TPA}$$ TPA ’s, as well. We prove that the equational theory of $$\mathsf{TPA}^-$$ TPA - is much simpler, namely, it is recursively enumerable. We also give motivation for our results and some connections to related work. (shrink)

We look at lower semilattice-ordered residuated semigroups and, in particular, the representable ones, i.e., those that are isomorphic to algebras of binary relations. We will evaluate expressions in representable algebras and give finite axiomatizations for several notions of validity. These results will be applied in the context of substructural logics.

In this paper we show that relativized versions of relation set algebras and cylindric set algebras have undecidable equational theories if we include coordinatewise versions of the counting operations into the similarity type. We apply these results to the guarded fragment of first-order logic.

The problem of whether Lambek Calculus is complete with respect to (w.r.t.) relational semantics, has been raised several times, cf. van Benthem (1989a) and van Benthem (1991). In this paper, we show that the answer is in the affirmative. More precisely, we will prove that that version of the Lambek Calculus which does not use the empty sequence is strongly complete w.r.t. those relational Kripke-models where the set of possible worlds,W, is a transitive binary relation, while that version of the (...) Lambek Calculus where we admit the empty sequence as the antecedent of a sequent is strongly complete w.r.t. those relational models whereW=U×U for some setU. We will also look into extendability of this completeness result to various fragments of Girard's Linear Logic as suggested in van Benthem (1991), p. 235, and investigate the connection between the Lambek Calculus and language models. (shrink)

We consider the problem of the product finite model property for binary products of modal logics. First we give a new proof for the product finite model property of the logic of products of Kripke frames, a result due to Shehtman. Then we modify the proof to obtain the same result for logics of products of Kripke frames satisfying any combination of seriality, reflexivity and symmetry. We do not consider the transitivity condition in isolation because it leads to infinity axioms (...) when taking products. (shrink)

The aim of this paper is to give a new proof for the decidability and finite model property of first-order logic with two variables (without function symbols), using a combinatorial theorem due to Herwig. The results are proved in the framework of polyadic equality set algebras of dimension two (Pse 2 ). The new proof also shows the known results that the universal theory of Pse 2 is decidable and that every finite Pse 2 can be represented on a finite (...) base. Since the class Cs 2 of cylindric set algebras of dimension 2 forms a reduct of Pse 2 , these results extend to Cs 2 as well. (shrink)

The aim of this paper is to give a new proof for the decidability and finite model property of first-order logic with two variables, using a combinatorial theorem due to Herwig. The results are proved in the framework of polyadic equality set algebras of dimension two. The new proof also shows the known results that the universal theory of Pse$_2$ is decidable and that every finite Pse$_2$ can be represented on a finite base. Since the class Cs$_2$ of cylindric set (...) algebras of dimension 2 forms a reduct of Pse$_2$, these results extend to Cs$_2$ as well. (shrink)

We prove that algebras of binary relations whose similarity type includes intersection, union, and one of the residuals of relation composition form a nonfinitely axiomatizable quasivariety and that the equational theory is not finitely based. We apply this result to the problem of the completeness of the positive fragment of relevance logic with respect to binary relations.

Demonic composition, demonic refinement and demonic union are alternatives to the usual ‘angelic’ composition, angelic refinement (inclusion) and angelic (usual) union defined on binary relations. We first motivate both the angelic and the demonic via an analysis of the behaviour of non-deterministic programs, with the angelic associated with partial correctness and demonic with total correctness, both cases emerging from a richer algebraic model of non-deterministic programs incorporating both aspects. Zareckiĭ has shown that the isomorphism class of algebras of binary relations (...) under angelic composition and inclusion is finitely axiomatized as the class of ordered semigroups. The proof can be used to establish that the same axiomatization applies to binary relations under demonic composition and refinement, and a further modification of the proof can be used to incorporate a zero element representing the empty relation in the angelic case and the full relation in the demonic case. For the signature of angelic composition and union, it is known that no finite axiomatization exists, and we show the analogous result for demonic composition and demonic union by showing that the same axiomatization holds for both. We show that the isomorphism class of algebras of binary relations with the ‘mixed’ signature of demonic composition and angelic inclusion has no finite axiomatization. As a contrast, we show that the isomorphism class of partial algebras of binary relations with the partial operation of constellation product and inclusion (also a ‘mixed’ signature) is finitely axiomatizable. (shrink)

We show that the variety of weakly representable relation algebras is neither canonical nor closed under Monk completions.

Value Oriented Science for A Sustainable Society The essay deals with the relationship between ethics, science and the character of society associated with challenges such as: What is the contemporary role of science in society and how does it fulfil it? Is value oriented "engaged" science possible? What does the responsibility of science mean? What is the reason for and the state of integrative, interdisciplinary, cross-disciplinary and/or post-disciplinary approaches in the science? What is the role and meaning of evaluation in (...) scientific production and/or its usefulness? What is the value, cost and effectiveness of science? Is scientometrics an adequate answer? What is the role of ethics and science in the context of sustainable development/living/society? In the final section of the essay several examples drawing on the international as well as the national level are introduced. The ambition of the author, a professional environmental geographer, is not to submit an extensive excursion into most fashionable aspects of the topic within the global philosophical context. The author describes his own personal experience and position and tries to discover what the emerging challenges and threats in this field may be, first of all in the current Slovak context. (shrink)

Violence in the world, explosive population growth, uneven and unfair distribution of wealth, destruction of the environment and/or the ineffectiveness of supranational political and economic tools and institutions and other problems are more and more achieving global character. The growth of number, frequency and intensity of global problems and threats is a reality. In the same time it represents a big challenge: How to find a generally acceptable, adequate global solution? The majority of political and intellectual leaders around the world (...) acknowledge concept of sustainable development/sustainable living as the most important tool for protecting the biosphere and for securing reasonable development for the future. The development and implementation of the sustainable living concept is driven by the effort to reach – as much as possible – the ideals of humanism and the harmony between man and nature, based on the respect of life. Values compatible with a sustainable way of living are a set of values, the implementation of which promote the shift towards sustainable future. These values are not completely new. Just the opposite. They create the core of the common heritage of humankind, since the oldest religious cultures. The submitted study tries to map the recent developments of values compatible with the sustainable way of living problematic from both Czech, Slovak and thinkers from abroad perspectives in the wider framework of relevant international activities. (shrink)

The origin of human language is one of the most fascinating and most difficult problems of evolution. Here I argue that pre-hunt communication was the starting context of the evolution of human language. Hunting of big game created a shared interest; animals and hunting actions are easy to imitate; the need to plan created a pressure for increasing complexity; and finally, cultural inheritance of hunting tools and know-how made the transition unique. I further argue that this “first step” was actually (...) a two-stage process where first indexical and iconic signs evolved to coordinate recruitment for the hunt; then later, in the second stage, the complexity of this communication system increased as a response to the increased demand to coordinate group-hunting effort (including division of labor). I provide a review of the fossil record and show that the available evidence is fully compatible with the theory. (shrink)

Weather imagery plays a major role in Hosea. Hosea 2 recalls the image of an unfaithful wife; Hosea 4:2-3 describes the withering of the land; in 6:3; 10:12; 14:6, the several types of precipitation draw attention to the utterance of YHWH or the requested righteousness; in 9:10.13.16; 10:1; 13:5; 14:6.8, Israel is symbolised by different plants that blossom and wither, depending on their relation to Yhwh. In all of these instances, weather phenomena contribute to these images. In this article, I (...) try to catalogue and evaluate the metaphors and concepts to look at how meteorological images convey theological and historical messages, and vice versa how historical events or sociological procedures demonstrate their consequences in nature, especially in the weather. It seems that weather imagery is used to describe the consequences of idolatry, injustice and false politics. These cause drought and famine in a concrete sense, but the withering of Israel figuratively, the last word of the book is a call for repentance that could ensure Israel's well-being once again. With these metaphors, Hosea explicitly delivers a plea for monolatry and righteousness, as well as for equality, in an implicit way. These pieces of evidence can provide a basis for further interpretation from the hermeneutical perspective of the notion called 'interconnectedness'. CONTRIBUTION: This article analyses the weather imagery of the Book of Hosea and contributes to a better understanding of the use of these metaphors in prophetic discourses. (shrink)

Traces of thoughts. The place of a theology of the Septuagint in biblical scholarship: In the past decades, research has raised the idea of a theology of the Septuagint (LXX) on various occasions. Important works were recently published on this topic in the Handbuch zur Septuaginta and the Septuagint and Cognate Studies series. The general theological tendencies of the LXX are identified by scholars in eschatology, messianism, anti-anthropomorphism and angelology. These tend to all be regarded as further developments of the (...) theology of the Hebrew Bible (HB). However, one can trace the evolution of these and other main topics of the LXX in the New Testament (NT) and in the later apostolic writings as well. Based on three concise case studies, I point out the evolution of theological ideas from the HB through the LXX up to the NT in this paper. First, I will discuss the importance of the ‘Name of God’-theology which is increasingly present in the LXX and has a key role in the messianic passages of the NT. Then in two points it will be argued that addressing Jesus as κύριος implies theological accents which can be detected in the LXX. These observations aim to show that the development of the religious ideologies of the HB can be followed not only in the LXX but in the NT and beyond as well. The importance of a theology of the LXX goes beyond the HB research, having significant implications for the NT as well. In fact, such theology could build the bridge between the HB and the NT, and should not only be written from the viewpoint of the HB but also considering the NT. Contribution: This contribution traces the routes of three theological concepts originating in the Hebrew Bible developed further in the LXX and finally adopted by the New Testament. Based on these three examples, it is suggested here as a novel idea that a theology of the LXX should not be written only with the Hebrew Bible in mind but also considering the New Testament. (shrink)

In the past decades, research has raised the idea of a theology of the Septuagint on various occasions. Important works were recently published on this topic in the Handbuch zur Septuaginta and the Septuagint and Cognate Studies series. The general theological tendencies of the LXX are identified by scholars in eschatology, messianism, anti-anthropomorphism and angelology. These tend to all be regarded as further developments of the theology of the Hebrew Bible. However, one can trace the evolution of these and other (...) main topics of the LXX in the New Testament and in the later apostolic writings as well. Based on three concise case studies, I point out the evolution of theological ideas from the HB through the LXX up to the NT in this paper. First, I will discuss the importance of the 'Name of God'-theology which is increasingly present in the LXX and has a key role in the messianic passages of the NT. Then in two points it will be argued that addressing Jesus as κύριος implies theological accents which can be detected in the LXX. These observations aim to show that the development of the religious ideologies of the HB can be followed not only in the LXX but in the NT and beyond as well. The importance of a theology of the LXX goes beyond the HB research, having significant implications for the NT as well. In fact, such theology could build the bridge between the HB and the NT, and should not only be written from the viewpoint of the HB but also considering the NT. CONTRIBUTION: This contribution traces the routes of three theological concepts originating in the Hebrew Bible developed further in the LXX and finally adopted by the New Testament. Based on these three examples, it is suggested here as a novel idea that a theology of the LXX should not be written only with the Hebrew Bible in mind but also considering the New Testament. (shrink)

The honesty of animal communication is in the spot lights in the last 30 years. During most of this time the field was dominated by one explanation: Zahavi’s handicap principle (Zahavi, J Theor Biol 67:603–605, 1975 ; Grafen, J Theor Biol 144:517–546, 1990 ). Grose (Biol Philos 2011 ) embarks to explain both the success of the theory and the empirical difficulties that exist despite this success. While I wholeheartedly agree with the criticism offered by Grose and with almost all (...) the claims he makes, the treatment of the issue is far from complete and it still leaves much to be explained. Accordingly, my commentary consist of six sections: in the first section I clear up some technical issues left unexposed, most importantly the role of strategic cost in handicap signalling; in the second section I relate this to empirical testing; in the next section I comment on the historical development of the handicap principle; in the fourth section I review the biological models that came up with conclusions that contradict the handicap principle; in the fifth section I discuss the reasons behind the success of the handicap theory; finally, in the last section I discuss the application of the handicap theory to anthropology and human sciences. (shrink)

The Enlightenment has often been written about as a sequence of disembodied 'great ideas'. The aim of this book is to put the beliefs of the Enlightenment firmly into their social context, by revealing the national soils in which they were rooted and the specific purposes for which they were used. It brings out the regional divergences of the Enlightenment experience, shaped by different local intellectual and economic priorities. At the same time it also shows how central concerns were shared (...) everywhere, and how the writings of certain key areas came to be influential elsewhere. The thirteen essays, each written by a historian specialising in the particular country, examine national contexts from Sweden to Italy, from Russia to North America. As well as focusing attention on the interplay of thought and action, ideology and society, the book offers important insights into the place of the intelligentsia in the modern world. (shrink)

In this commentary I argue that the notion of incommensurability can be extended to the child's developing theories of mind. I use Carey's concept of Quinian bootstrapping and show that this learning process can account for the acquisition of the semantics of mental terms. I suggest a distinction among three stages of acquisition and adopt the theory–theory of conceptual development.

Glossolalia (“speaking in tongues”) is a rhythmic utterance of word‐like strings of sounds, regularly occurring in religious mass gatherings or various forms of private religious practices (e.g., prayer and meditation). Although specific verbal learning capacities may characterize glossolalists, empirical evidence is lacking. We administered three statistical learning tasks (artificial grammar, phoneme sequence, and visual‐response sequence) to 30 glossolalists and 30 matched control volunteers. In artificial grammar, participants decide whether pseudowords and sentences follow previously acquired implicit rules or not. In sequence (...) learning, they gradually draw out rules from repeating regularities in sequences of speech sounds or motor responses. Results revealed enhanced artificial grammar and phoneme sequence learning performances in glossolalists compared to control volunteers. There were significant positive correlations between daily glossolalia activity and artificial grammar learning. These results indicate that glossolalists exhibit enhanced abilities to extract the statistical regularities of verbal information, which may be related to their unusual language abilities. (shrink)

Cognitive Science, Volume 46, Issue 7, July 2022.

An increasing number of Muslim asylum seekers and refugees convert to Christianity in Europe. The conversion motifs in these individuals are unknown. In this study, we applied biographical interviews in 124 converts. There were two dominant patterns: intellectual —intellectual plus experimental motifs, and mystical —mystical plus affectional motifs. Pure experimental and affectional motifs were rare, and there were no revivalist and coercive motifs. Demographic parameters did not predict conversion motifs. We found no evidence for social pressure. These results indicate that (...) finding meaning and consolation in Christian religious teachings and mystical experiences with a high emotional content are the two leading religious conversion motifs. (shrink)

Human language and human music are both unique communication systems that evolved in the human lineage. Here, I propose that they share the same root, they evolved from an ancestral communication system yet to be described in detail. I suggest that pre-hunt charade was this shared root, which helped organize and coordinate the hunt of early hominins.

Essential Buddhism, the fundamental teachings of the historical Buddha and the core of all major branches of Buddhism, is psychology, not religion or philosophy. Essential Buddhism is described from a psychological perspective and interrelated with Western psychology in general, and cognitive science, behaviour modification, psychoanalysis, and transpersonal psychology, in specific. Integrating Buddhist psychology and Western psychology yields a more comprehensive psychology and more powerful therapies.