ABSTRACT In this paper we introduce a set of six logical values, arising in the application of three-valued logics to time intervals, find its algebraic structure, and use it to define a six-valued logic. We then prove, by using algebraic properties of the class of De Morgan algebras, that this semantically defined logic can be axiomatized as Belnap's ?useful? four-valued logic. Other directions of research suggested by the construction of this set of six logical values are described.

The innovation systems approach has swiftly spread out worldwide in the last three decades and stood as an important framework for policy-making in the fields of science, technology, and innovation. At the same time, there have been serious and untreated concerns in the literature about the theoretical soundness of this approach. Our discussion in this paper is based on the belief that a detailed analysis on epistemological foundations of the approach could shed a judgmental light on the aforementioned concerns. To (...) provide that analysis, we reconstructed and studied the nature and evolution of innovation systems approach as a case of conceptual revolution against the more established traditions in economics of innovation. Our analyses show that the rise of the systemic view of innovation include radical changes in conceptual structures pertaining to orthodox view of innovation. These developments also go so far as to include significant shifts in epistemological foundations of the old paradigm. These later shifts provide us with an epistemological base from which we can shelter the innovation systems approach from the hard criticisms rooted in a quasi-positivist point of view. That epistemological base also shows the path for the future development of the approach towards more robustness and precision. (shrink)

Morally supererogatory actions are traditionally conceived of as actions that are nonobligatory but distinctively morally worthy. Here I challenge the assumption that supererogatory actions are distinctively praiseworthy and offer an alternative definition of moral supererogation. This alternative definition complements, and is complemented by, a novel account of moral praiseworthiness, which I call the Two-Step view. My Two-Step view of moral worth, which I develop in some detail, accounts for currently underappreciated features of moral praiseworthiness.

A study of smooth classes whose generic structures have simple theory is carried out in a spirit similar to Hrushovski 147; Simplicity and the Lascar group, preprint, 1997) and Baldwin–Shi 1). We attach to a smooth class K0, of finite -structures a canonical inductive theory TNat, in an extension-by-definition of the language . Here TNat and the class of existentially closed models of =T+,EX, play an important role in description of the theory of the K0,-generic. We show that if M (...) is the K0,-generic then MEX. Furthermore, if this class is an elementary class then Th=Th). The investigations by Hrushovski and Pillay , provide a general theory for forking and simplicity for the nonelementary classes, and using these ideas, we show that if K0,, where {,*}, has the joint embedding property and is closed under the Independence Theorem Diagram then EX is simple. Moreover, we study cases where EX is an elementary class. We introduce the notion of semigenericity and show that if a K0,-semigeneric structure exists then EX is an elementary class and therefore the -theory of K0,-generic is near model complete. By this result we are able to give a new proof for a theorem of Baldwin and Shelah 1359). We conclude this paper by giving an example of a generic structure whose first-order theory is simple. (shrink)

We study smooth classes without the algebraic closure property. For such smooth classes we investigate the simplicity of the class of generic structures, in the context of Robinson theories.

We prove that for any simple theory which is constructed via Fräissé-Hrushovski method, if the forking independence is the same as the d-independence then the stable forking property holds.

We prove that for any simple theory which is constructed via Fräissé-Hrushovski method, if the forking independence is the same as the d-independence then the stable forking property holds.

Pentecostal Republic: Religion and the Struggle for State Power in Nigeria By ObadareEbenezer, xviii + 214 pp. Price PB £16.99. EAN 978–1786992376.

Generalizing Woodin’s extender algebra, cf. e.g. Steel (in: Kanamori (ed) Handbook of set theory, Springer, Berlin, 2010), we isolate the long extender algebra as a general version of Bukowský’s forcing, cf. Bukovský (Fundam Math 83:35–46, 1973), in the presence of a supercompact cardinal.

We study invariant measures on compact Hausdorff spaces using finitary integral logic. For each compact Hausdorff space X and any family equation image of its continuous transformations, we find equivalent conditions for the existence of an equation image-invariant measure on X. We give two proofs of the existence of Haar measure on compact groups.

There are two types of stock price manipulation examined in the theoretical literature: insider trading, which involves private information that is true and the public spreading of fraudulent false information. While there is a large empirical literature on insider trading, this is the first empirical article to examine the impact of false, fraudulent public information on stock prices and trading volume. We find that such false information, even after being denied by a credible source such as the SEC, generates both (...) abnormal returns and abnormal trading volume. We also find that the effects of the false information on security returns and volume can be persistent for at least 2 weeks. In addition, we show that perpetrators of false news attacks can make potentially large profits from such market manipulations. (shrink)

We develop a model theoretic framework for studying algebraic structures equipped with a measure. The real line is used as a value space and its usual arithmetical operations as connectives. Integration is used as a quantifier. We extend some basic results of pure model theory to this context and characterize measurable sets in terms of zero-sets of formulas.

In a relational language consisting of a single relation R, we investigate pseudofiniteness of certain Hrushovski constructions obtained via predimension functions. It is notable that the arity of the relation R plays a crucial role in this context. When R is ternary, by extending the methods recently developed by Brody and Laskowski, we interpret 〈Q+,<〉 in the 〈K+,≤∗〉-generic and prove that this structure is not pseudofinite. This provides a negative answer to the question posed in an earlier work by Evans (...) and Wong. This result, in fact, unfolds another aspect of complexity of this structure, along with undecidability and the strict order property proved in the mentioned earlier works. On the other hand, when R is binary, it can be shown that the 〈K+,≤∗〉-generic is decidable and pseudofinite. (shrink)

We prove an omitting types theorem and one direction of the related Ryll-Nardzewski theorem for semi-classical theories introduced in [2].

In this paper, we introduce a foundation for computable model theory of rational Pavelka logic and continuous logic, and prove effective versions of some related theorems in model theory. We show how to reduce continuous logic to rational Pavelka logic. We also define notions of computability and decidability of a model for logics with computable, but uncountable, set of truth values; we show that provability degree of a formula with respect to a linear theory is computable, and use this to (...) carry out an effective Henkin construction. Therefore, for any effectively given consistent linear theory in continuous logic, we effectively produce its decidable model. This is the best possible, since we show that the computable model theory of continuous logic is an extension of computable model theory of classical logic. We conclude with noting that the unique separable model of a separably categorical and computably axiomatizable theory is decidable. (shrink)

A value space is a topological algebra equipped with a non-empty family of continuous quantifiers . We will describe first-order logic on the basis of . Operations of are used as connectives and its relations are used to define statements. We prove under some normality conditions on the value space that any theory in the new setting can be represented by a classical first-order theory.