In [9] we introduced a new framework for asymptotic probabilities, in which a $\sigma-additive$ measure is defined on the sample space of all sequences $A = $ of finite models, where the universe of An is {1, 2, .., n}. In this framework we investigated the strong 0-1 law for sentences, which states that each sentence either holds in An eventually almost surely or fails in An eventually almost surely. In this paper we define the strong convergence law for formulas, (...) which carries over the ideas of the strong 0-1 law to formulas with free variables, and roughly states that for each formula φ(x), the fraction of tuples a in An, which satisfy the formula φ(x), almost surely has a limit as n tends to infinity. We show that the infinitary logic with finitely many variables has the strong convergence law for formulas for the uniform measure, and further characterize the measures on random graphs for which the strong convergence law holds. (shrink)

We introduce a new framework for asymptotic probabilities of sentences, in which we have a σ-additive measure on the sample space of all sequences A = {A n } of finite models, where the universe of A n is {1,2... n}, and use this framework to strengthen 0-1 laws for logics.

We introduce a new framework for asymptotic probabilities of sentences, in which we have a σ-additive measure on the sample space of all sequencesA= {} of finite models, where the universe ofis {1,2, …, n}. and use this framework to strengthen 0-1 laws for logics.

The relation between free will and necessity is one of the most important issues regarding the problem of “free will”. This is because of the rule which indicates that “being not necessary, an event would not be came off”. There has been an ongoing debate among theologians, philosophers and Jurists on whether this rule includes free actions. Sadrain Philosophers believe that this rule is inclusive of human free actions, while followers of the Na’eeni school endorse the opposite. In this article, (...) after reviewing the views of philosophers and jurists on the stages of a free action, I shall explore the question whether human actions, stages of which are understood deterministic, could be regarded as free, and so, whether Na’eenian criticisms against philosophers are justified. Besides, I shall put forth some innovative ideas of Allameh Ja’fari concerning the issue, whose view, while revises some philosophers’, is not compatible with that of Na’eeni. (shrink)

Our research extends the current understanding of cognitive moral reasoning research by considering the often‐overlooked element of context, specifically the issue presented in the ethical dilemma, and the issue of gender agreement between the subject and the dilemma actor. We rely on gender identity and cognitive moral reasoning theories to provide the theoretical underpinnings of our exploration to deepen our understanding of the contextual forces affecting cognitive moral reasoning. Our results generally confirm earlier research findings and provide valuable information regarding (...) our understanding of the impact of the dilemma context and the gender agreement or disagreement between the subject and the actor in an ethical dilemma, with significance found for four of our five hypotheses, with half of the significant results in the direction predicted. Implications for future academic research and business practice are discussed. (shrink)

For each truth-functionally complete set of connectives, we construct a sound and complete natural deduction system containing no axioms and the smallest possible number of inference rules, namely one.

We obtain an almost everywhere quantifier elimination for (the noncritical fragment of) the logic with probability quantifiers, introduced by the first author in [10]. This logic has quantifiers like $\exists ^{ \ge 3/4} y$ which says that "for at least 3/4 of all y". These results improve upon the 0-1 law for a fragment of this logic obtained by Knyazev [11]. Our improvements are: 1. We deal with the quantifier $\exists ^{ \ge r} y$ , where y is a tuple (...) of variables. 2. We remove the closedness restriction, which requires that the variables in y occur in all atomic subformulas of the quantifier scope. 3. Instead of the unbiased measure where each model with universe n has the same probability, we work with any measure generated by independent atomic probabilities pR for each predicate symbol R. 4. We extend the results to parametric classes of finite models (for example, the classes of bipartite graphs, undirected graphs, and oriented graphs). 5. We extend the results to a natural (noncritical) fragment of the infinitary logic with probability quantifiers. 6. We allow each pR , as well as each r in the probability quantifier $(\exists ^{ \ge r} y)$ , to depend on the size of the universe. (shrink)

The response to feeding needs in advanced dementia patients is a subject of ethical inquiry. Advanced dementia is the debilitating result of a range of neurodegenerative diseases. As this terminal illness progresses, patients develop mild to severe dysphagia that can make swallowing difficult. Of the two available options, artificial tube feeding or oral hand feeding, an estimated one-third of these patients will receive artificial tube feeding. However, observational studies have failed to validate the clinical benefits of tube feeding. Ethics of (...) care, the feminist philosophical perspective, and Ubuntu philosophy offer arguments for the choice of oral hand-feeding as a preferrable first option by caregivers as far as possible. These moral theories acknowledge that human beings can be dependent for long periods, mostly early and later years of life. Both views reflect an approach that draws people into a system of interdependent caring relationships. They encourage hand feeding as a way of exhibiting solidarity and respecting human dignity even at the end of life. (shrink)

We prove a local normal form theorem of the Gaifman type for the infinitary logic L∞ωω whose formulas involve arbitrary unary quantifiers but finite quantifier rank. We use a local Ehrenfeucht-Fraïssé type game similar to the one in [9]. A consequence is that every sentence of L∞ωω of quantifier rank n is equivalent to an infinite Boolean combination of sentences of the form ψ, where ψ has counting quantifiers restricted to the -neighborhood of y.

This paper introduces a new Ehrenfeucht-Fraïssé type game that is played on two classes of models rather than just two models. This game extends and generalizes the known Ajtai-Fagin game to the case when there are several alternating moves played in different models. The game allows Duplicator to delay her choices of the models till the very end of the game, making it easier for her to win. This adds on the toolkit of winning strategies for Duplicator in Ehrenfeucht-Fraïssé type (...) games and opens up new methods for tackling some open problems in descriptive complexity theory. As an application of the class game, it is shown that, if m is a power of a prime, then first order logic augmented with function quantifiers F1n of arity 1 and height n < m can not express that the size of the model is divisible by m. This, together with some new expressibility results for Henkin quantifiers H1n gives some new separation results on the class of finite models among various F1n on one hand and between F1n and H1n on the other. Since function quantifiers involve a bounded type of second order existential quantifiers, the class game solves an open problem raised by Fagin, which asks for some inexpressibility result using a winning strategy by Duplicator in a game that involves more than one coloring round. (shrink)

This paper studies the expressive power that an extra first order quantifier adds to a fragment of monadic second order logic, extending the toolkit of Janin and Marcinkowski [JM01].We introduce an operation existsn on properties S that says "there are n components having S". We use this operation to show that under natural strictness conditions, adding a first order quantifier word u to the beginning of a prefix class V increases the expressive power monotonically in u. As a corollary, if (...) the first order quantifiers are not already absorbed in V, then both the quantifier alternation hierarchy and the existential quantifier hierarchy in the positive first order closure of V are strict.We generalize and simplify methods from Marcinkowski [Mar99] to uncover limitations of the expressive power of an additional first order quantifier, and show that for a wide class of properties S, S cannot belong to the positive first order closure of a monadic prefix class W unless it already belongs to W.We introduce another operation alt on properties which has the same relationship with the Circuit Value Problem as reach has with the Directed Reachability Problem. We use alt to show that Πn⊈ FO, Σn⊈ FO, and Δn+1⊈ FOB, solving some open problems raised in [Mat98]. (shrink)

Gaifman's normal form theorem showed that every first-order sentence of quantifier rank n is equivalent to a Boolean combination of “scattered local sentences”, where the local neighborhoods have radius at most 7n−1. This bound was improved by Lifsches and Shelah to 3×4n−1. We use Ehrenfeucht–Fraïssé type games with a “shrinking horizon” to get a spectrum of normal form theorems of the Gaifman type, depending on the rate of shrinking. This spectrum includes the result of Lifsches and Shelah, with a more (...) easily understood proof and with the bound on the radius improved to 4n−1. We also obtain bounds for a normal form theorem of Schwentick and Barthelmann. (shrink)

We give an axiomatization of first‐order logic enriched with the almost‐everywhere quantifier over finitely additive measures. Using an adapted version of the consistency property adequate for dealing with this generalized quantifier, we show that such a logic is both strongly complete and enjoys Craig interpolation, relying on a (countable) model existence theorem. We also discuss possible extensions of these results to the almost‐everywhere quantifier over countably additive measures.

We prove a local normal form theorem of the Gaifman type for the infinitary logic L∞ωω whose formulas involve arbitrary unary quantifiers but finite quantifier rank. We use a local Ehrenfeucht-Fraïssé type game similar to the one in [9]. A consequence is that every sentence of L∞ωω of quantifier rank n is equivalent to an infinite Boolean combination of sentences of the form ψ, where ψ has counting quantifiers restricted to the -neighborhood of y.

Human neoplasms develop following the progressive accumulation of genetic and epigenetic alterations to oncogenes and tumor suppressor genes. These alterations confer a growth advantage to the cancer cell, leading to its clonal proliferation, invasion into surrounding tissues, and spread to distant organs. Genes that are altered in neoplasia affect three major biologic pathways that normally regulate cell growth and tissue homeostasis: the cell cycle, apoptosis, and differentiation. While each of these pathways can be defined by a unique set of molecular (...) events, they are not biologically separate. Rather, they function more as an integrated molecular network, and perturbations in one pathway can have profound consequences on another. Insights into what distinguishes the regulation of growth and differentiation in a normal cell versus a cancer cell have led to the development of novel anticancer therapies. BioEssays 24:83–90, 2002. © 2002 John Wiley & Sons, Inc. (shrink)

Los soberanos de la dinastía Naṣrí de Granada se intitulan sultanes o Amīr al-Muslimīn en su abundante correspondencia exterior con otros príncipes musulmanes o cristianos. Sin embargo, a partir de la segunda dinastía, comienzan a utilizar también el título califal aunque parece que de forma privada, dentro del entorno familiar o el cortesano, tal como prueban determinados documentos emanados del Dīwān al-Inšā’ naṣrí. El califato ostentado por los Naṣríes no es el mismo que el de los Omeyas o los Almohades (...) que llevaba emparejado el título de Amīr al-Mu’minīn y Jalīfat Rasūl Allāh, sino que lo acompañan del título de Jalīfat al-Raḥmān o Jalīfat Allāh, como otros soberanos musulmanes de la baja Edad Media. Su legitimidad está basada en una genealogía que les hace entroncar con los Jazārŷ, es decir con los Anṣār de Sa‘d b. ‘Ubāda, que pretendió proclamarse Califa a la muerte de Muḥammad. (shrink)

Ibn al-Khatīb is mainly known as a litterateur, but he was also an engaged politician who held the office of vizier in the Nasri kingdom of Grenada. His political ideas were related to his wish to justify his involvement in political affairs and, in particular, his position as a powerful vizier.