The aim of my paper is to clarify the conceptions of epistemic deism and probabilistic theism and to demonstrate that the two doctrines do not finally collapse into one. I would like also to point some reasons for the acceptance of a certain version of probabilistic theism which I will call in the last part of the article “open probabilistic theism”. Open probabilistic theism is not a version of the view called “open theism”. The reasons for the openness of open (...) probabilistic theism are quite different from the reasons supporting open theism. (shrink)

Models and modelling are central not only to management but to all human affairs. Models provide grounds for decision making and action-taking. This paper investigates the concept of ‘model’, showing that the conventional notion of a model as understood in management science, a notion founded on positivism and realism, is insufficient for the complex practical needs of management models. To remedy this situation, an alternative notion founded on Projective Constructivist Epistemology (PCE) is proposed. Some of the implications of the new (...) notion for modelling practice and model validation are also discussed. The new notion results from theoretical investigations and empirical experience gleaned over the last five years in public-sector, military and business contexts. The paper concludes with a brief discussion of areas that might merit investigation in the future. (shrink)

We present new probabilistic generalizations of Pearl’s entailment in System Z and Lehmann’s lexicographic entailment, called Zλ- and lexλ-entailment, which are parameterized through a value λ ∈ [0,1] that describes the strength of the inheritance of purely probabilistic knowledge. In the special cases of λ = 0 and λ = 1, the notions of Zλ- and lexλ-entailment coincide with probabilistic generalizations of Pearl’s entailment in System Z and Lehmann’s lexicographic entailment that have been recently introduced by the author. We show (...) that the notions of Zλ- and lexλ-entailment have similar properties as their classical counterparts. In particular, they both satisfy the rationality postulates of System P and the property of Rational Monotonicity. Moreover, Zλ-entailment is weaker than lexλ-entailment, and both Zλ- and lexλ-entailment are proper generalizations of their classical counterparts. (shrink)

O logice Stoików pisali Prantl, Zeller, Brochard. Żaden z nich nie zrozumiał tej logiki, bo żaden z nich nie miał dostatecznego wykształcenia logicznego. Co prawda, nie można im nawet robić z tego zarzutu, bo skądże się mieli logiki nauczyć? Sądy ich o logice stoickiej nie mają żadnej wartości. Dopiero dziś wiemy, dzięki logice matematycznej, że logika Stoików jest systemem całkowicie różnym od syllogistyki Arystotelesa. Logika stoicka bowiem jest odpowiednikiem dzisiejszej "teorji dedu...

We propose a combination of probabilistic reasoning from conditional constraints with approaches to default reasoning from conditional knowledge bases. In detail, we generalize the notions of Pearl's entailment in system Z, Lehmann's lexicographic entailment, and Geffner's conditional entailment to conditional constraints. We give some examples that show that the new notions of z-, lexicographic, and conditional entailment have similar properties like their classical counterparts. Moreover, we show that the new notions of z-, lexicographic, and conditional entailment are proper generalizations of (...) both their classical counterparts and the classical notion of logical entailment for conditional constraints. (shrink)

La logique des stoïciens a été déjà étudiée par Prantl, Zeller et Brochard. Aucun d’entre eux ne l’a comprise, car aucun n’avait de formation suffisante en logique. Il est vrai que cela ne peut même pas leur être reproché, car, après tout, où pouvaient-ils l’apprendre? Leurs jugements sur la logique stoïcienne n’ont aucune valeur. Ce n’est qu’aujourd’hui que nous savons, grâce à la logique mathématique, que la logique des stoïciens est un système entièrement différent de la syllogistique d’A...

We study probabilistic logic under the viewpoint of the coherence principle of de Finetti. In detail, we explore how probabilistic reasoning under coherence is related to model- theoretic probabilistic reasoning and to default reasoning in System . In particular, we show that the notions of g-coherence and of g-coherent entailment can be expressed by combining notions in model-theoretic probabilistic logic with concepts from default reasoning. Moreover, we show that probabilistic reasoning under coherence is a generalization of default reasoning in System (...) . That is, we provide a new probabilistic semantics for System , which neither uses infinitesimal probabilities nor atomic bound (or big-stepped) probabilities. These results also provide new algorithms for probabilistic reasoning under coherence and for default reasoning in System , and they give new insight into default reasoning with conditional objects. (shrink)

The ability to conduct logical reasoning is a fundamental aspect of intelligent behavior, and thus an important problem along the way to human-level artificial intelligence. Traditionally, symbolic methods from the field of knowledge representation and reasoning have been used to equip agents with capabilities that resemble human reasoning qualities. More recently, however, there has been an increasing interest in applying alternative approaches based on machine learning rather than logic-based formalisms to tackle this kind of tasks. Here, we make use of (...) state-of-the-art methods for training deep neural networks to devise a novel model that is closely coupled to symbolic reasoning methods, and thus able to learn how to effectively perform basic ontology reasoning. This term describes an important and at the same time very natural kind of problem settings where the rules for conducting reasoning are specified alongside with the actual information. Many problems in practice may be viewed as such reasoning tasks, which is why the presented approach is applicable to a plethora of important real-world problems. To demonstrate the effectiveness of the suggested method, we present the outcomes of several experiments that have been conducted on both toy datasets as well as real-world data, which show that our model learned to perform precise reasoning on a number of diverse inference tasks that require comprehensive deductive proficiencies. Furthermore, it turned out that the suggested model suffers much less from different obstacles that prohibit symbolic reasoning. (shrink)

The ability to conduct logical reasoning is a fundamental aspect of intelligent behavior, and thus an important problem along the way to human-level artificial intelligence. Traditionally, symbolic methods from the field of knowledge representation and reasoning have been used to equip agents with capabilities that resemble human reasoning qualities. More recently, however, there has been an increasing interest in applying alternative approaches based on machine learning rather than logic-based formalisms to tackle this kind of tasks. Here, we make use of (...) state-of-the-art methods for training deep neural networks to devise a novel model that is closely coupled to symbolic reasoning methods, and thus able to learn how to effectively perform basic ontology reasoning. This term describes an important and at the same time very natural kind of problem settings where the rules for conducting reasoning are specified alongside with the actual information. Many problems in practice may be viewed as such reasoning tasks, which is why the presented approach is applicable to a plethora of important real-world problems. To demonstrate the effectiveness of the suggested method, we present the outcomes of several experiments that have been conducted on both toy datasets as well as real-world data, which show that our model learned to perform precise reasoning on a number of diverse inference tasks that require comprehensive deductive proficiencies. Furthermore, it turned out that the suggested model suffers much less from different obstacles that prohibit symbolic reasoning. (shrink)

In the discussion at hand I have attempted to pave the way for such a treatment of the principle of contradiction. In a number of respects it seems to me worthwhile to relate my critical exposition to Aristotle's train of thought. Indeed, every critique must be raised against something substantial, otherwise it generally becomes the critic's leisurely game with his own cerebral phantasies. Now Aristotle's intuitions regarding the principle of contradiction are, for the most part and clear down to the (...) present day, the usual and traditional ones; and arguments for and against the principle can be found together in the Stagirite in greater completeness than in any one modern textbook of logic. My investigation will proceed with the Aristotelian text at hand and with regard to the results of symbolic logic. The most important results shall be sketched very briefly in the following. (shrink)

This study analyzes a complex case in society, namely, how to distinguish ride-sharing applications, such as Uber, from ordinary taxi enterprises. We conduct a structural analysis of normative practices with distinctions at the following levels: aspects; radical types, genotypes, and phenotypes; part-whole, enkaptic relationships, and interlinkages; and the distinction between qualifying and foundational functions as it is captured in the theory of normative practices. We conclude that the genotype of taxi matchmaking enterprises, of which Uber is an example, represents a (...) novel normativity that could positively serve society and also produce normative challenges, depending on its governance. Therefore, regulators should not dismiss the entire genotype of taxi matchmaking enterprises, but should address the phenotypes that are illegal or that cannot thrive without the illegal behaviors of its users. This conclusion is clear from the structural and directional sides of the practice. (shrink)