How should physical entities be characterized? Physicalists, who have most to do with the notion, usually characterize the physical by reference to two components: 1. The physical entities are the entities treated by fundamental physics with the proviso that 2. Physical entities are not fundamentally mental (that is, do not individually possess or bestow mentality) Here I explore the extent to which the appeals to fundamental physics and to the NFM (“no fundamental mentality”) constraint are appropriate for characterizing the physical, (...) especially for purposes of formulating physicalism. Ultimately, I motivate and defend a version of an account incorporating both components: The physics-based NFM account: An entity existing at a world w is physical iff (i) it is treated, approximately accurately, by current or future (in the limit of inquiry, ideal) versions of fundamental physics at w, and (ii) it is not fundamentally mental (that is, does not individually either possess or bestow mentality). (shrink)

An important component in the interventionist account of causal explanation is an interpretation of counterfactual conditionals as statements about consequences of hypothetical interventions. The interpretation receives a formal treatment in the framework of functional causal models. In Judea Pearl’s influential formulation, functional causal models are assumed to satisfy a “unique-solution” property; this class of Pearlian causal models includes the ones called recursive. Joseph Halpern showed that every recursive causal model is Lewisian, in the sense that from the causal model one (...) can construct a possible worlds model in David Lewis’s well-known semantics that satisfies the exact same formulas in a certain language. Moreover, he demonstrated that some Pearlian (non-recursive) models are not Lewisian in this sense. This raises the question regarding the exact contour of Lewisian causal models. In this paper, we provide a characterization of the class of Lewisian causal models and a complete axiomatization with respect to this class. Our results have philosophically interesting consequences, two of which are especially worth noting. First, the class of Stalnakerian causal models, a subclass of Lewisian causal models, is precisely the class of Pearlian models that do not contain any cycle of counterfactual dependence (in a sense of counterfactual dependence akin to Lewis’s famous relation between distinct events). Second, a more natural class of causal models is actually a superclass of Lewisian causal models, the logic of which respects only weak centering rather than centering. (shrink)

Ordinal analysis is a research program wherein recursive ordinals are assigned to axiomatic theories. According to conventional wisdom, ordinal analysis measures the strength of theories. Yet what is the attendant notion of strength? In this paper we present abstract characterizations of ordinal analysis that address this question. -/- First, we characterize ordinal analysis as a partition of $\Sigma^1_1$-definable and $\Pi^1_1$-sound theories, namely, the partition whereby two theories are equivalent if they have the same proof-theoretic ordinal. We show that no equivalence (...) relation $\equiv$ is finer than the ordinal analysis partition if both: (1) $T\equiv U$ whenever $T$ and $U$ prove the same $\Pi^1_1$ sentences; (2) $T\equiv T+U$ for every set $U$ of true $\Sigma^1_1$ sentences. In fact, no such equivalence relation makes a single distinction that the ordinal analysis partition does not make. -/- Second, we characterize ordinal analysis as an ordering on arithmetically-definable and $\Pi^1_1$-sound theories, namely, the ordering wherein $T\leq U$ if the proof-theoretic ordinal of $T$ is less than or equal to the proof-theoretic ordinal of $U$. The standard ways of measuring the strength of theories are consistency strength and inclusion of $\Pi^0_1$ theorems. We introduce analogues of these notions---$\Pi^1_1$-reflection strength and inclusion of $\Pi^1_1$ theorems---in the presence of an oracle for $\Sigma^1_1$ truths, and prove that they coincide with the ordering induced by ordinal analysis. (shrink)

The reason for characterizing mental states as propositional attitudes is sentence form: ‘S Vs that p’. However, many mental states are not ascribed by means of such sentences, and the sentences that ascribe them cannot be appropriately paraphrased. Moreover, even if a paraphrase were always available, that in itself would not establish the characterization. And the mental states that are ascribable by appropriate senses do not form any natural subset of mental states. A reason for the characterization relying (...) on beliefs, etc., about non‐existing things is also rejected. Last, some sentences ascribing abilities and dispositions have the same grammatical form as some senses that ascribe mental states, so that the attempt to paraphrase the latter would obscure the conceptual relations between the two sorts. It follows that mental states are not relations to propositions. (shrink)

How should we understand validity? A standard way to characterize validity is in terms of the preservation of truth (or truth in a model). But there are several problems facing such characterizations. An alternative approach is to characterize validity epistemically, for instance in terms of the preservation of an epistemic status. In this paper, I raise a problem for such views. First, I argue that if the relevant epistemic status is factive, such as being in a position to know or (...) having conclusive evidence for, then the account runs into trouble if we endorse certain familiar logical principles. Second, I argue that if the relevant epistemic status is non-factive, such as is rationally committed to or has justification for believing, then a similar problem arises if we endorse the logical principles as well as a sufficiently strong epistemic “level-bridging” principle. Finally, I argue that an analogous problem arises for the most natural characterization of validity in terms of rational credence. (shrink)

We show that three fundamental information-theoretic constraints -- the impossibility of superluminal information transfer between two physical systems by performing measurements on one of them, the impossibility of broadcasting the information contained in an unknown physical state, and the impossibility of unconditionally secure bit commitment -- suffice to entail that the observables and state space of a physical theory are quantum-mechanical. We demonstrate the converse derivation in part, and consider the implications of alternative answers to a remaining open question about (...) nonlocality and bit commitment. (shrink)

It is proved that $\Pi^1_1$ -indescribability in $P_{\kappa}\lambda$ can be characterized by combinatorial properties without taking care of cofinality of $\lambda$ . We extend Carr's theorem proving that the hypothesis $\kappa$ is $2^{\lambda^{<\kappa}}$ -Shelah is rather stronger than $\kappa$ is $\lambda$ -supercompact.

Critical reflection on clinical ethics consultation is essential to the field. Johnson and colleagues (2015) have helpfully summarized the consultation experience of a children's specialty hospital...

Mundici has recently established a characterization of free finitely generated MV-algebras similar in spirit to the representation of the free Boolean algebra with a countably infinite set of free generators as any Boolean algebra that is countable and atomless. No reference to universal properties is made in either theorem. Our main result is an extension of Mundici’s theorem to the whole class of MV-algebras that are free over some finite distributive lattice.

In this paper, a complex non- linear programming problem with the two parts (real and imaginary) is considered. The efficient and proper efficient solutions in terms of optimal solutions of related appropriate scalar optimization problems are characterized. Also, the Kuhn-Tuckers' conditions for efficiency and proper efficiency are derived. This paper is divided into two independently parts: The first provides the relationships between the optimal solutions of a complex single-objective optimization problem and solutions of two related real programming problems. The second (...) part is concerned with the theory of a multi-objective optimization in complex space. (shrink)

An adequate semantics for generic sentences must stake out positions across a range of contested territory in philosophy and linguistics. For this reason the study of generic sentences is a venue for investigating different frameworks for understanding human rationality as manifested in linguistic phenomena such as quantification, classification of individuals under kinds, defeasible reasoning, and intensionality. Despite the wide variety of semantic theories developed for generic sentences, to date these theories have been almost universally model-theoretic and representational. This essay outlines (...) a range of proof-theoretic analyses for characterizing generics. Particular attention is given to an expressivist proof-theory that can be traced to 1) work on logical syntax that Carnap undertook prior to his turn toward truth-conditional model theory in the late 1930s, and 2) research on sequent calculi and natural deduction systems that originate in work from Gentzen and Prawitz.1. (shrink)

Inductively defined structures are ubiquitous in mathematics; their specification is unambiguous and their properties are powerful. All fields of mathematical logic feature these structures prominently: the formula of a language, the set of theorems, the natural numbers, the primitive recursive functions, the constructive number classes and segments of the cumulative hierarchy of sets. -/- This dissertation gives a mathematical characterization of a species of inductively defined structures, called accessible domains, which include all of the above examples except the set (...) of theorems. The concept of an accessible domain comes from Wilfried Sieg's analysis of proof-theoretic practices, starting with his dissertation. In particular, he noticed the special epistemological character of elements of an accessible domain: they can always be uniquely identified with their build-up. Generally, the unique build-up of elements justifies the principles of induction and recursion. -/- I use category theory to give an abstract characterization of accessible domains. I claim that accessible domains are all instances of initial algebras for endofunctors. Grounded in the historical roots of Sieg's discussions, this dissertation shows how the properties of initial algebras for endofunctors and accessible domains coincide in a satisfying and natural way. -/- Filling out this characterization, I show how important examples of accessible domains fit into this broad characterization. I first characterize some accessible domains by relatively simple functors (e.g. finite, polynomial, those that preserve certain colimits) where we can see how iterating the functor can produce the accessible domain. Then I describe accessible domains that result from more involved specifications (e.g. ordinals and segments of the cumulative hierarchies associated with CZF, IZF, and ZF) by relying heavily on algebraic set theory. I end with a discussion of some of the methodological features of category theory in particular that helped characterize accessible domains. (shrink)

We characterize the existence of semicontinuous weak utilities in a general framework, where the axioms of transitivity and acyclicity are relaxed to that of consistency in the sense of Suzumura (Economica 43:381–390, 1976). This kind of representations allow us to transfer the problem of the existence of the ${{\mathcal{G}}{\mathcal{O}}{\mathcal{C}}{\mathcal{H}}{\mathcal{A}}}$ set of a binary relation to the easier problem of getting maxima of a real function. Finally, we show that the maxima of these representations correspond to the different levels of satiation (...) that each of individual has (an individual reaches his or her level of satiation when an increase of consuming an alternative product/service brings no increase in utility). (shrink)

The disciplinary characterisation (DC) is the most popular approach to defining metaphysical naturalism and physicalism. It defines metaphysical naturalism with reference to scientific theories and defines physicalism with reference to physical theories, and suggests that every entity that exists is a posited entity of these theories. DC has been criticised for its inability to solve Hempel’s dilemma and a list of problems alike. In this paper, I propose and defend a novel version of DC that can be called a historical (...) paths approach. The idea is (roughly) that metaphysical naturalism can be defined with reference to the historical ideas that current scientific ideas descend from. I argue that it is not rendered implausible by the above problems, and hence that DC is more defensible and attractive than it may first appear. I then argue that the approach also provides a useful framework for the naturalisation of the philosophy of mind and phenomenology. (shrink)

Over the last decade, several extensions of Dung’s Abstract Argumentation Frameworks (AFs) have been introduced in the literature. Some of these extensions concern the nature of the attack relation, such as the consideration of recursive attacks, whereas others incorporate additional interactions, such as a support relation. Recently, the Attack–Support Argumentation Framework (ASAF) was proposed, which accounts for recursive attacks and supports, attacks to supports and supports to attacks, at any level, where the support relation is interpreted as necessity. Currently, to (...) determine the accepted elements of an ASAF (which may be arguments, attacks, and supports) it is required to translate such an ASAF into a Dung’s AF. In this work, we provide a formal characterization of acceptability semantics directly on the ASAF, without requiring such a translation. We prove that our characterization is sound since it satisfies different results from Dung’s argumentation theory; moreover, we formally show that the approach proposed here for addressing acceptability is equivalent to the preexisting one, in which the ASAF was translated into an AF. Also, we formalize the relationship between the ASAF and other frameworks on which it is inspired: the Argumentation Framework with Recursive Attacks (AFRA) and the Argumentation Framework with Necessities (AFN). (shrink)

In this paper we mainly study preservation theorems for two fragments of the infinitary languagesLκκ, withκregular, without the equality symbol: the universal Horn fragment and the universal strict Horn fragment. In particular, whenκisω, we obtain the corresponding theorems for the first-order case.The universal Horn fragment of first-order logic (with equality) has been extensively studied; for references see [10], [7] and [8]. But the universal Horn fragment without equality, used frequently in logic programming, has received much less attention from the model (...) theoretic point of view. At least to our knowledge, the problem of obtaining preservation results for it has not been studied before by model theorists. In spite of this, in the field of abstract algebraic logic we find a theorem which, properly translated, is a preservation result for the strict universal Horn fragment of infinitary languages without equality which, apart from function symbols, have only a unary relation symbol. This theorem is due to J. Czelakowski; see [5], Theorem 6.1, and [6], Theorem 5.1. A. Torrens [12] also has an unpublished result dealing with matrices of sequent calculi which, properly translated, is a preservation result for the strict universal Horn fragment of a first-order language. And in [2] of W. J. Blok and D. Pigozzi we find Corollary 6.3 which properly translated corresponds to our Corollary 19, but for the case of a first-order language that apart from its function symbols has only oneκ-ary relation symbol, and for strict universal Horn sentences. The study of these results is the basis for the present work. In the last part of the paper, Section 4, we will make these connections clear and obtain some of these results from our theorems. In this way we hope to make clear two things: (1) The field of abstract algebraic logic can be seen, in part, as a disguised study of universal Horn logic without equality and so has an added interest. (2) A general study of universal Horn logic without equality from a model theoretic point of view can be of help in the field of abstract algebraic logic. (shrink)

We present a general construction of a □κ-sequence in Jensen's fine structural extender models. This construction yields a local definition of a canonical □κ-sequence as well as a characterization of those cardinals κ, for which the principle □κ fails. Such cardinals are called subcompact and can be described in terms of elementary embeddings. Our construction is carried out abstractly, making use only of a few fine structural properties of levels of the model, such as solidity and condensation.

The human masticatory system is a complex functional unit characterized by a multitude of skeletal components, muscles, soft tissues, and teeth. Muscle activation dynamics cannot be directly measured on live human subjects due to ethical, safety, and accessibility limitations. Therefore, estimation of muscle activations and their resultant forces is a longstanding and active area of research. Reinforcement learning (RL) is an adaptive learning strategy which is inspired by the behavioral psychology and enables an agent to learn the dynamics of an (...) unknown system via policy-driven explorations. The RL framework is a well-formulated closed-loop system where high capacity neural networks are trained with the feedback mechanism of rewards to learn relatively complex actuation patterns. In this work, we are building on a deep RL algorithm, known as the Soft Actor-Critic, to learn the inverse dynamics of a simulated masticatory system, i.e., learn the activation patterns that drive the jaw to its desired location. The outcome of the proposed training procedure is a parametric neural model which acts as the brain of the biomechanical system. We demonstrate the model’s ability to navigate the feasible three-dimensional (3D) envelope of motion with sub-millimeter accuracies. We also introduce a performance analysis platform consisting of a set of quantitative metrics to assess the functionalities of a given simulated masticatory system. This platform assesses the range of motion, metabolic efficiency, the agility of motion, the symmetry of activations, and the accuracy of reaching the desired target positions. We demonstrate how the model learns more metabolically efficient policies by integrating a force regularization term in the RL reward. We also demonstrate the inverse correlation between the metabolic efficiency of the models and their agility and range of motion. The presented masticatory model and the proposed RL training mechanism are valuable tools for the analysis of mastication and other biomechanical systems. We see this framework’s potential in facilitating the functional analyses aspects of surgical treatment planning and predicting the rehabilitation performance in post-operative subjects. (shrink)

Afacan (Games and Economic Behavior 110: 71-89, 2018) introduces an object allocation with random priorities problem. He proposes the constrained probabilistic serial (CPS) mechanism. This study, for the first time in the literature, provides axiomatic characterizations of CPS. The first result characterizes it via non-wastefulness, claimwise stability, constrained ordinal fairness, and surplus invariance to truncations. The other axiomatizes CPS via constrained stochastic efficiency, claimwise stability, and constrained ordinal fairness. The independence of the axioms is provided.

Jude Edeh ABSTRACT: The challenge faced with the proliferation of various kinds of cognitivism is the difficulty of providing a straightforward characterization of moral realism and antirealism. In light of this tension, I identified a problem in Sayre-McCord’s way of specifying the criteria of moral realism. Furthermore, I provided a framework that characterized the moral ….

Este trabajo tiene como objetivo caracterizar el proceso de evaluación del aprendizaje del contenido estadístico en la carrera de Medicina. Los resultados obtenidos evidencian que el nivel de asimilación alcanzado por los estudiantes en muchas ocasiones es el reproductivo, lo que refleja la necesidad de seguir profundizando en los estudios de esta problemática. Issues related to the learning evaluation have been present throughout the teaching learning process history. The following research aims at characterizing the learning process of evaluation of the (...) statistical content in medicine. Results demonstrate that the assimilation level reached by students, on many occasions, is the reproductive one, as a need to deepen on methodology of the design of the system of evaluation of the statistical content learning in medicine. (shrink)

El Ministerio de Salud Pública cubano ha otorgado especial importancia al tema relacionado con el desempeño profesional evaluativo de la información estadística en los profesionales de la salud, pero una revisión bibliográfica permitió constatar el insuficiente debate pedagógico encaminado a diagnosticar su estado actual para proponer alternativas que permitan su formación y desarrollo en los estudiantes. Este artículo tiene como objetivo caracterizar el desempeño profesional evaluativo de la información estadística en estudiantes de Medicina. Los resultados obtenidos con la aplicación de (...) métodos y técnicas de investigación, tales como encuestas, test de conocimientos permitieron confirmar que ese desempeño actualmente se expresa a un nivel insatisfactorio de actuación. Se concluyó buscar formas más efectivas para su logro en estudiantes de Medicina. The Cuban Ministry of Public Health has given special importance to the subject of professional assessment of statistical information in the area of public health; however, a bibliographic review allowed authors to prove pedagogical debate unsatisfactory. The review was aimed at diagnosing its current state and therefore provide alternatives that allow its formation and development in medical students. The objective of the article is to characterize the assessable professional performance of statistical information in medical students. The results achieved through the application of research methods and techniques such as surveys and knowledge tests enabled to confirm that, nowadays, professional performance is below satisfactory performance levels. As a result, newer and more effective ways of achieving it in medical students will be searched for. (shrink)

Normative characterization is a commonplace feature of biological and cognitive explanation. Such language seems to commit the biological and cognitive sciences to the existence of natural norms, but it is also difficult to understand how such normativity fits into a natural world of physical causes and forces. I propose to map normativity onto systems stabilized by counteractive constraints. Such a mapping, I believe, can explain normativity’s causal-explanatory role in biological and cognitive inquiry. The common approach in the literature is (...) to derive an account of natural normativity by way of a particular theory of function. I avoid that approach here and attempt to address directly the sort of physical systems that might satisfy naturalizing criteria for normativity. This has the advantages, I think, of allowing an account of normativity without first having to decide the correct theory of function as well as allowing for the theoretical possibility that normative and functional explanation might come apart within empirical explanation. (shrink)

In a voting context, when the preferences of voters are described by linear orderings over a finite set of alternatives, the Maximin rule orders the alternatives according to their minimal rank in the voters’ preferences. It is equivalent to the Fallback bargaining process described by Brams and Kilgour (Group Decision and Negotiation 10:287–316, 2001). This article proposes a characterization of the Maximin rule as a social welfare function (SWF) based upon five conditions: Neutrality, Duplication, Unanimity, Top Invariance, and Weak (...) Separability. In a similar way, we obtain a characterization for the Maximax SWF by using Bottom Invariance instead of Top Invariance. Then, these results are compared to the axiomatic characterizations of two famous scoring rules, the Plurality rule and the Antiplurality rule. (shrink)

Three thoughts strongly influence recent work on sensory imagination, often without explicit articulation. The image thought says that all mental states involving a mental image are imaginative. The attitude thought says that, if there is a distinctive imaginative attitude, it is a single, monolithic attitude. The function thought says that the functions of sensory imagination are identical or akin to functions of other mental states such as judgment or belief. Taken together, these thoughts create a theoretical context within which eliminativism (...) appears attractive. Eliminativism is the idea that we needn’t refer to a distinctive attitude in order to characterize sensory imagination: the attitudes involved in other states provide all the resources we need. Peter Langland-Hassan’s account of sensory imagination provides an example of such eliminativism. Via close examination of this account, I make manifest the three thoughts and their collective tendency to support eliminativism. I argue that all three are dubious, and that we should reject eliminativism; we need a distinctive imaginative attitude if we are to adequately explicate sensory imagination. (shrink)

We report a quantitative analysis of the cross-utterance coordination observed in child-directed language, where successive utterances often overlap in a manner that makes their constituent structure more prominent, and describe the application of a recently published unsupervised algorithm for grammar induction to the largest available corpus of such language, producing a grammar capable of accepting and generating novel wellformed sentences. We also introduce a new corpus-based method for assessing the precision and recall of an automatically acquired generative grammar without recourse (...) to human judgment. The present work sets the stage for the eventual development of more powerful unsupervised algorithms for language acquisition, which would make use of the coordination structures present in natural child-directed speech. (shrink)

This paper gives an implicit characterization of the class of functions computable in polynomial space by deterministic Turing machines – PSPACE. It gives an inductive characterization of PSPACE with no ad-hoc initial functions and with only one recursion scheme. The main novelty of this characterization is the use of pointers to reach PSPACE. The presence of the pointers in the recursion on notation scheme is the main difference between this characterization of PSPACE and the well-known Bellantoni-Cook (...) characterization of the polytime functions – PTIME. (shrink)

Two-dimensional coupled map lattices display, in a specific parameter range, a stable phase (quasi-) periodic in both space and time. With small changes to the model parameters, this stable phase develops spontaneous eruptions of nonperiodic behavior. Although this behavior itself appears irregular, it can be characterized in a systematic fashion. In particular, parameter-independent features of the spontaneous eruptions may allow useful empirical characterizations of other phenomena that are intrinsically hard to predict and reproduce. Specific features of the distributions of lifetimes (...) and emergence rates of irregular states display such parameter-independent properties. Ó 2004 Elsevier Ltd. All rights reserved. (shrink)

Consider predicates like 'is a fictional character' and 'is a mythical object'. Since their ascription entails a corresponding Negative Existential claim, call these 'NE-characterizing predicates'. Objectualists such as Parsons, Sylvan, van Inwagen, and Zalta think that NE-characterizing properties are genuine properties of genuinely non-existent objects. But how, then, to make room for statements like 'Vulcan is a failed posit' and 'that little green man is a trick of the light'? The predicates involved seem equally NE-characterizing yet on the surface fail (...) to mark a genuine property o f things. Instead, the truth of such predications strongly supervenes on types of referential failure. Kendall Walton's anti-objectualist account of talk about fiction provides a neat solution to this supervenience problem by invoking special games of make-believe. The present paper claims that while Walton's view thereby gains an important advantage over objectualism, the solution faces problems of its own. The rest of the paper desribes another solution, one that assigns a large role to the idea of metaphor. (shrink)

This paper is a contribution to graded model theory, in the context of mathematical fuzzy logic. We study characterizations of classes of graded structures in terms of the syntactic form of their first-order axiomatization. We focus on classes given by universal and universal-existential sentences. In particular, we prove two amalgamation results using the technique of diagrams in the setting of structures valued on a finite MTL-algebra, from which analogues of the Łoś–Tarski and the Chang–Łoś–Suszko preservation theorems follow.

Martin's axiom is equivalent to the statement that the universe is absolute under ccc forcing extensions for Σ 1 sentences with a subset of $\kappa, \kappa , as a parameter.

Forensic evidence often involves an evaluation of whether two impressions were made by the same source, such as whether a fingerprint from a crime scene has detail in agreement with an impression taken from a suspect. Human experts currently outperform computer-based comparison systems, but the strength of the evidence exemplified by the observed detail in agreement must be evaluated against the possibility that some other individual may have created the crime scene impression. Therefore, the strongest evidence comes from features in (...) agreement that are also not shared with other impressions from other individuals. We characterize the nature of human expertise by applying two extant metrics to the images used in a fingerprint recognition task and use eye gaze data from experts to both tune and validate the models. The Attention via Information Maximization model quantifies the rarity of regions in the fingerprints to determine diagnosticity for purposes of excluding alternative sources. The CoVar model captures relationships between low-level features, mimicking properties of the early visual system. Both models produced classification and generalization performance in the 75%–80% range when classifying where experts tend to look. A validation study using regions identified by the AIM model as diagnostic demonstrates that human experts perform better when given regions of high diagnosticity. The computational nature of the metrics may help guard against wrongful convictions, as well as provide a quantitative measure of the strength of evidence in casework. (shrink)

This article investigates the properties of multistate top revision, a dichotomous model of belief revision that is based on an underlying model of probability revision. A proposition is included in the belief set if and only if its probability is either 1 or infinitesimally close to 1. Infinitesimal probabilities are used to keep track of propositions that are currently considered to have negligible probability, so that they are available if future information makes them more plausible. Multistate top revision satisfies a (...) slightly modified version of the set of basic and supplementary AGM postulates, except the inclusion and success postulates. This result shows that hyperreal probabilities can provide us with efficient tools for overcoming the well known difficulties in combining dichotomous and probabilistic models of belief change. (shrink)

This article presents important properties of standard discrete distributions and its conjugate densities. The Bernoulli and Poisson processes are described as generators of such discrete models. A characterization of distributions by mixtures is also introduced. This article adopts a novel singular notation and representation. Singular representations are unusual in statistical texts. Nevertheless, the singular notation makes it simpler to extend and generalize theoretical results and greatly facilitates numerical and computational implementation.

We generalize the Unstable Formula Theorem characterization of stable theories from Shelah [11], that a theory T is stable just in case any infinite indiscernible sequence in a model of T is an indiscernible set. We use a generalized form of indiscernibles from [11], in our notation, a sequence of parameters from an L-structure M, , indexed by an L′-structure I is L′-generalized indiscernible inM if qftpL′=qftpL′ implies tpL=tpL for all same-length, finite ¯,j from I. Let Tg be the (...) theory of linearly ordered graphs in the language with signature Lg={<,R}. Let Kg be the class of all finite models of Tg. We show that a theory T has NIP if and only if any Lg-generalized indiscernible in a model of T indexed by an Lg-structure with age equal to Kg is an indiscernible sequence. (shrink)

Featuring contributions from the world’s leading experts on the subject and based partly on several detailed case studies, this volume is the first comprehensive analysis of the scientific notion of robustness as well as of the general ...

In [14] we used the term finitely algebraizable for algebraizable logics in the sense of Blok and Pigozzi [2] and we introduced possibly infinitely algebraizable, for short, p.i.-algebraizable logics. In the present paper, we characterize the hierarchy of protoalgebraic, equivalential, finitely equivalential, p.i.-algebraizable, and finitely algebraizable logics by properties of the Leibniz operator. A Beth-style definability result yields that finitely equivalential and finitely algebraizable as well as equivalential and p.i.-algebraizable logics can be distinguished by injectivity of the Leibniz operator. Thus, (...) from a characterization of equivalential logics we obtain a new short proof of the main result of [2] that a finitary logic is finitely algebraizable iff the Leibniz operator is injective and preserves unions of directed systems. It is generalized to nonfinitary logics. We characterize equivalential and, by adding injectivity, p.i.-algebraizable logics. (shrink)