We consider several kinds of partition relations on the set ${\mathbb{R}}$ of real numbers and its powers, as well as their parameterizations with the set ${[\mathbb{N}]^{\mathbb{N}}}$ of all infinite sets of natural numbers, and show that they hold in some models of set theory. The proofs use generic absoluteness, that is, absoluteness under the required forcing extensions. We show that Solovay models are absolute under those forcing extensions, which yields, for instance, that in these models for every well ordered partition (...) of ${\mathbb{R}^\mathbb{N}}$ there is a sequence of perfect sets whose product lies in one piece of the partition. Moreover, for every finite partition of ${[\mathbb{N}]^{\mathbb{N}} \times \mathbb{R}^{\mathbb{N}}}$ there is ${X \in [\mathbb{N}]^{\mathbb{N}}}$ and a sequence ${\{P_{k} : k \in \mathbb{N}\}}$ of perfect sets such that the product ${[X]^{\mathbb{N}} \times \prod_{k}^{\infty}P_{k}}$ lies in one piece of the partition, where ${[X]^{\mathbb{N}}}$ is the set of all infinite subsets of X. The proofs yield the same results for Borel partitions in ZFC, and for more complex partitions in any model satisfying a certain degree of generic absoluteness. (shrink)

In 1979, H. Lewis shows that the computational complexity of the Boolean satisfiability problem dichotomizes, depending on the Boolean operations available to formulate instances: intractable (NP-complete) if negation of implication is definable, and tractable (in P) otherwise [21]. Recently, an investigation in the same spirit has been extended to nonclassical propositional logics, modal logics in particular [2, 3]. In this note, we pursue this line in the realm of many-valued propositional logics, and obtain complexity classifications for the parameterized (...) satisfiability problem of two pertinent samples, Kleene and Gödel logics. (shrink)

In this paper we consider a natural generalization of the Principle of Instantial Relevance and give a complete characterization of the probabilistic belief functions satisfying this principle as a family of discrete probability functions parameterized by a single real δ ∊ [0, 1).

The Anderson-Friedman absolute objects program has been a favorite analysis of the substantive general covariance that supposedly characterizes Einstein's General Theory of Relativity (GTR). Absolute objects are the same locally in all models (modulo gauge freedom). Substantive general covariance is the lack of absolute objects. Several counterexamples have been proposed, however, including the Jones-Geroch dust and Torretti constant curvature spaces counterexamples. The Jones-Geroch dust case, ostensibly a false positive, is resolved by noting that holes in the dust in some models (...) ensure that no physically relevant nonvanishing timelike vector field exists there, so no absolute object exists. The Torretti constant curvature spaces case, allegedly a false negative, is resolved by testing an irreducible piece of the metric, the conformal metric density of weight -2/3, for absoluteness; this geometric object is absolute. A new counterexample is proposed involving the orthonormal tetrad said to be necessary to couple spinors to a curved metric. The threat of finding an absolute object in GTR + spinors is overcome by the use of an alternative spinor formalism that takes a symmetric square root of the metric (with the help of the matrix diag(-1,1,1,1)), eliminating 6 of the 16 tetrad components as irrelevant. The importance of eliminating irrelevant structures, as Anderson emphasized, is clear. The importance of the choice of physical fields is also evident. A new counterexample due to Robert Geroch and Domenico Giulini, however, finds an absolute object in vacuum GTR itself, namely the scalar density $g$ given by the metric components' determinant. Thus either the definition of absoluteness or its use to analyze GTR's substantive general covariance is flawed. Anderson's belief that all absolute objects are nonvariational (that is, not varied in a suitable action principle) and vice versa is also falsified by the Geroch-Giulini counterexample. However, it remains plausible that all nonvariational fields are absolute, so adding nonvariationality as a necessary condition for absoluteness, as Hiskes once suggested, would likely leave no useful work to the Anderson-Friedman condition of sameness in all models. Simply having only variational fields in an action principle (suitably free of irrelevant fields) might be a satisfactory analysis of substantive general covariance, if one exists. This proposal also resembles the suggestion that GTR is "already parameterized," if one decides to parameterize theories by defining the nonvariational fields in terms of preferred coordinates called clock fields. More questions need to be addressed. Which fields should be tested for absoluteness: only primitive fields (which ones?), or all or some (which?) of their concomitants also? Geroch observes that some kinds of geometric objects, such as tangent vectors, scalar densities, and tangent vector densities of non-unit weight, satisfy the condition of sameness in all models if they merely fail to vanish. If these "susceptible" geometric objects can hardly help being absolute, to what degree are they, or the theories harboring them, responsible for this absoluteness? The answer to this question helps to determine the significance of the Geroch-Giulini counterexample. (shrink)

Sufficient conditions for first-order-based sequent calculi to admit cut elimination by a Schütte–Tait style cut elimination proof are established. The worst case complexity of the cut elimination is analysed. The obtained upper bound is parameterized by a quantity related to the calculus. The conditions are general enough to be satisfied by a wide class of sequent calculi encompassing, among others, some sequent calculi presentations for the first order and the propositional versions of classical and intuitionistic logic, classical and intuitionistic (...) modal logic S4, and classical and intuitionistic linear logic and some of its fragments. Moreover the conditions are such that there is an algorithm for checking if they are satisfied by a sequent calculus. (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)

Applying the solutions defined in the axiomatic bargaining theory to actual bargaining problems is a challenge when the problem is not described by its Utility Possibility Set (UPS) but as a social choice environment specifying the set of alternatives and utility profile underlying the UPS. It requires computing the UPS, which is an operational challenge, and then identifying at least one alternative that actually achieves the bargained solution’s outcome. We introduce the axioms of Independence of Non-Strongly-Efficient Alternatives (resp. Weakly) and (...) Independence of Redundant Alternatives. A solution satisfying these axioms can be applied to a simplified problem based on any reduced set of alternatives generating the strong (resp. weak) Pareto frontier of the initial problem, without changing the outcome, making the application of bargaining solutions to actual problems easier. We compare our axioms to usual independence axioms, and discuss their consistency with usual bargaining solutions. Then, we introduce monotonicity conditions corresponding to the existence of an interest group, i.e., agents ranking the alternatives in the same order. For such monotonic social choice environments, we provide a parameterized family of alternatives that generates the Pareto frontier of the bargaining problem, in line with our previous results. Our analysis illustrates that an axiomatic approach can be useful to foster the application of bargaining solutions, in complement to usual computational methods. (shrink)

. Computational chemistry grew in a new era of “desktop modeling,” which coincided with a growing demand for modeling software, especially from the pharmaceutical industry. Parameterization of models in computational chemistry is an arduous enterprise, and we argue that this activity leads, in this specific context, to tensions among scientists regarding the epistemic opacity transparency of parameterized methods and the software implementing them. We relate one flame war from the Computational Chemistry mailing List in order to assess in detail (...) the relationships between modeling methods, parameterization, software and the various forms of their enclosure or disclosure. Our claim is that parameterization issues are an important and often neglected source of epistemic opacity and that this opacity is entangled in methods and software alike. Models and software must be addressed together to understand the epistemological tensions at stake. (shrink)

Many parameterized problems ask, given an instance and a natural number k as parameter, whether there is a solution of size k. We analyze the relationship between the complexity of such a problem and the corresponding maximality problem asking for a solution of size k maximal with respect to set inclusion. As our results show, many maximality problems increase the parameterized complexity, while “in terms of the W-hierarchy” minimality problems do not increase the complexity. We also address the (...) corresponding construction, listing, and counting problems. (shrink)

Parameterized complexity has, so far, been largely confined to consideration of computational problems as decision or search problems. However, it is becoming evident that the parameterized point of view can lead to new insight into counting problems. The goal of this article is to introduce a formal framework in which one may consider parameterized counting problems.

Theory of mind refers to the human capacity for reasoning about others’ mental states based on observations of their actions and unfolding events. This type of reasoning is notorious in the cognitive science literature for its presumed computational intractability. A possible reason could be that it may involve higher-order thinking. To investigate this we formalize theory of mind reasoning as updating of beliefs about beliefs using dynamic epistemic logic, as this formalism allows to parameterize ‘order of thinking.’ We prove that (...) theory of mind reasoning, so formalized, indeed is intractable. Using parameterized complexity we prove, however, that the ‘order parameter’ is not a source of intractability. We furthermore consider a set of alternative parameters and investigate which of them are sources of intractability. We discuss the implications of these results for the understanding of theory of mind. (shrink)

We have parameterized Einstein’s thought experiment with atomic clocks, supposing that we knew neither if the space and time are relative or absolute, nor if the speed of light was ultimate speed or not. We have obtained a Parameterized Special Theory of Relativity (PSTR) (1982). Our PSTR generalized not only Einstein’s Special Theory of Relativity, but also our Absolute Theory of Relativity, and introduced three more possible Relativities to be studied in the future. After the 2011 CERN’s superluminal (...) neutrino experiments, we recall our ideas and invite researchers to deepen the study of PSTR, ATR, and check the three new mathematically emerged Relativities 4.3, 4.4, and 4.5. (shrink)

Mental model ascription – also called mindreading – is the process of inferring the mental states of others, which happens as a matter of course in social interactions. But although ubiquitous, mindreading is presumably a highly variable process: people mindread to different extents and with _different results._ We hypothesize that human mindreading ability relies on a large number of personal and contextual features: the inherent abilities of specific individuals, their current physical and mental states, their knowledge of the domain of (...) discourse, their familiarity with the interlocutor, the risks associated with an incorrect assessment of intent, and so on. This paper presents a theory of mindreading that models diverse artificial intelligent agents using an inventory of parameters and value sets that represent traits of humans and features of discourse contexts. Examples are drawn from Maryland Virtual Patient, a prototype system that will permit medical trainees to diagnose and treat cognitively modeled virtual patients with the optional assistance of a virtual tutor. Since real patients vary greatly with respect to physiological and cognitive features, so must a society of virtual patients. Modeling such variation is one of the goals of the overall OntoAgent program of research and development. (shrink)

Thomas Richardson and Peter Spirtes. Parameterizing and Scoring Mixed Ancestral Graphs.

Mental model ascription – also called mindreading – is the process of inferring the mental states of others, which happens as a matter of course in social interactions. But although ubiquitous, mindreading is presumably a highly variable process: people mindread to different extents and with different results. We hypothesize that human mindreading ability relies on a large number of personal and contextual features: the inherent abilities of specific individuals, their current physical and mental states, their knowledge of the domain of (...) discourse, their familiarity with the interlocutor, the risks associated with an incorrect assessment of intent, and so on. This paper presents a theory of mindreading that models diverse artificial intelligent agents using an inventory of parameters and value sets that represent traits of humans and features of discourse contexts. Examples are drawn from Maryland Virtual Patient, a prototype system that will permit medical trainees to diagnose and treat cognitively modeled virtual patients with the optional assistance of a virtual tutor. Since real patients vary greatly with respect to physiological and cognitive features, so must a society of virtual patients. Modeling such variation is one of the goals of the overall OntoAgent program of research and development. (shrink)

Automated reasoning issues are addressed for a finite lattice-valued propositional logic LnP(X) with truth-values in a finite lattice-valued logical algebraic structure—lattice implication algebra. We investigate extended strategies and rules from classical logic to LnP(X) to simplify the procedure in the semantic level for testing the satisfiability of formulas in LnP(X) at a certain truth-value level α (α-satisfiability) while keeping the role of truth constant formula played in LnP(X). We propose a lock resolution method at a certain truth-value level (...) α (α-lock resolution) in LnP(X) and have proved its theorems of soundness and weak completeness, respectively. We provide more efficient resolution based automated reasoning in LnP(X) and key supports for α-resolution-based automated reasoning approaches and algorithms in lattice based linguistic truth-valued logic. (shrink)

Sparse languages play an important role in classical structural complexity theory. In this paper we introduce a natural definition of sparse problems for parameterized complexity theory. We prove an analog of Mahaney's theorem: there is no sparse parameterized problem which is hard for the tth level of the W hierarchy, unless the W hierarchy itself collapses up to level t. The main result is proved for the most general form of parametric many:1 reducibility, where the parameter functions are (...) not assumed to be recursive. This provides one of the few instances in parameterized complexity theory of a full analog of a major classical theorem. The proof involves not only the standard technique of left sets, but also substantial circuit combinatorics to deal with the problem of small weft, and a diagonalization to cope with potentially nonrecursive parameter functions. The latter techniques are potentially of interest for further explorations of parameterized complexity analogs of classical structural results. (shrink)

We develop a dimension theory for D-semianalytic sets over an arbitrary non-Archimedean complete field. Our main results are the equivalence of several notions of dimension and a theorem on additivity of dimensions of projections and fibers in characteristic 0. We also prove a parameterized version of normalization for D-semianalytic sets.

In this article, I argue that desire-satisfaction theories of well-being face the problem of trivially satisfied desires. First, I motivate the claim that desire-satisfaction theories need an aggregation principle and reconstruct four possible principles desire-satisfactionists can adopt. Second, I contend that one of these principles seems implausible on numerous counts. Third, I argue that the other three principles, which hold that the creation and satisfaction of new desires is good for individuals and can be called proliferationist, are vulnerable to an (...) objection from trivially satisfied desires. They implausibly imply that forming desires that are trivially satisfied is good for individuals. Finally, I argue that trivially satisfied desires may also worsen desire-satisfactionism's classical problem of pointless desires. Together, these claims constitute a challenge to desire-satisfactionism. (shrink)

We have two main objections to Kerr and Godfrey-Smith's (2002) meticulous analysis. First, they misunderstand the position we took in Unto Others – we do not claim that individual-level statements about the evolution of altruism are always unexplanatory and always fail to capture causal relationships. Second, Kerr and Godfrey-Smith characterize the individual and the multi-level perspectives in terms of different sets of parameters. In particular, they do not allow the multi-level perspective to use the individual fitness parameters i and i. (...) We don't see why the multi-level perspective prevents one from thinking in these terms. Kerr and Godfrey-Smith's argument that Uyenoyama and Feldman's (1980, 1992) definition of altruism belongs more to the individualist perspective than it does to the multi-level perspective is an artifact of their choice of parameters; the same point applies to their argument about the individualism inherent in the idea of Class I and Class II fitness structures. (shrink)

Parameterization and parameter tuning are central aspects of climate modeling, and there is widespread consensus that these procedures involve certain subjective elements. Even if the use of these subjective elements is not necessarily epistemically problematic, there is an intuitive appeal for replacing them with more objective (automated) methods, such as machine learning. Relying on several case studies, we argue that, while machine learning techniques may help to improve climate model parameterization in several ways, they still require expert judgment that involves (...) subjective elements not so different from the ones arising in standard parameterization and tuning. The use of machine learning in parameterizations is an art as well as a science and requires careful supervision. (shrink)

We investigate the application of Courcelle’s theorem and the logspace version of Elberfeld et al. in the context of non-monotonic reasoning. Here we formalize the implication problem for propositional sets of formulas, the extension existence problem for default logic, the expansion existence problem for autoepistemic logic, the circumscriptive inference problem, as well as the abduction problem in monadic second order logic and thereby obtain fixed-parameter time and space efficient algorithms for these problems. On the other hand, we exhibit, for each (...) of the above problems, families of instances of a very simple structure that, for a wide range of different parameterizations, do not have efficient fixed-parameter algorithms (even in the sense of the large class XPnu, resp., XLnu) under standard complexity assumptions. (shrink)

The English language has adopted the word Tardis for something that looks simple from the outside but is much more complicated when inspected from the inside. The word comes from a BBC science fiction series, in which the Tardis is a machine for traveling in time and space, that looks like a phone booth from the outside. This paper claims that simulation models are a Tardis in a way that calls into question their transferability. The argument is developed taking Molecular (...) Modeling and Simulation as an example. There, simulation models are force fields that describe the molecular interactions and that look like simple and highly modular mathematical expressions. To make them work, they contain parameters that are adjusted to match certain data. The role of these parameters and the way they are obtained is seriously under-appreciated. It is constitutive for the model and central for its applicability and performance. Hence, the model is more than it seems so that working with adjustable parameters deeply affects the ontology of simulation models. This is particularly crucial for the transferability of the models: the information on how a model was trained is like luggage the model must carry on its voyage. (shrink)

A completeness theory for parameterized computational complexity has been studied in a series of recent papers, and has been shown to have many applications in diverse problem domains including familiar graph-theoretic problems, VLSI layout, games, computational biology, cryptography, and computational learning [ADF,BDHW,BFH, DEF,DF1-7,FHW,FK]. We here study the parameterized complexity of two kinds of problems: (1) problems concerning parameterized computations of Turing machines, such as determining whether a nondeterministic machine can reach an accept state in \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} (...) \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $k$\end{document} steps (the Short TM Computation Problem), and (2) problems concerning derivations and factorizations, such as determining whether a word \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $x$\end{document} can be derived in a grammar \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $G$\end{document} in \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $k$\end{document} steps, or whether a permutation has a factorization of length \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $k$\end{document} over a given set of generators. We show hardness and completeness for these problems for various levels of the \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $W$\end{document} hierarchy. In particular, we show that Short TM Computation is complete for \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $W[1]$\end{document}. This gives a new and useful characterization of the most important of the apparently intractable parameterized complexity classes. (shrink)

Many natural computational problems have input consisting of two or more parts, one of which may be considered a parameter. For example, there are many problems for which the input consists of a graph and a positive integer. A number of results are presented concerning parameterized problems that can be solved in complexity classes below P, given a single word of advice for each parameter value. Different ways in which the word of advice can be employed are considered, and (...) it is shown that the class FPT of tractable parameterized problems has interesting and natural internal structure. (shrink)

Satisfiability or Sat\ is the metatheoretic statementEvery formally intuitionistically consistent set of first-order sentences has a model.The models in question are the Tarskian relational structures familiar from standard first-order model theory, but here treated within intuitionistic metamathematics. We prove that both IZF, intuitionistic Zermelo–Fraenkel set theory, and HAS, second-order Heyting arithmetic, prove Sat\ to be false outright. Following the lead of Carter :75–95, 2008), we then generalize this result to some provably intermediate first-order logics, including the Rose logic. These (...) metatheorems distinguish the intuitionistic foundational significance of Sat\ sharply from that of Sat\, the satisfiability claim for intuitionistic propositional logic. At the same time, they establish intuitionistic connections with and between Test, COMP\, and \. Here, Test is the scheme of Testability, and COMP\ and \ are completeness for intuitionistic propositional logic and predicate logic, respectively. (shrink)

Leibniz said with a mixture of admiration and inspiration that the Duchess Sophie of Hannover always wanted to know the reason why behind the reason why. And that is just how rationality works: it wants to leave no loose ends to understanding, seeking to enable us to understand things through to the bitter end. In the twelve chapters that make up Satisfying Reason, Rescher develops and defends the following perspective: That rationality is a cardinal virtue in cognitive matters. That this (...) is not something simple and cut-and-dried: in the pursuit of truth through the development of knowledge we face obstacles -- sometimes even insuperable ones. All that we can do is the best we can, realizing that even our very best may still be imperfect. Nevertheless, the venture is far from hopeless. While absolutes are unattainable in the cognitive venture, some solutions are situationally optimal, being comparatively the best that can be managed under the circumstances. That reason itself enables us to come to terms with this state of affairs, urging us to accept the best we can do as good enough. Satisfying Reason is an explanation of the presuppositions and methods of rational enquiry, an original exercise in metaknowledge, developing a systematic body of knowledge about the scope and limits of knowledge itself. (shrink)

Propositional logic has been recognized throughout the centuries as one of the cornerstones of reasoning in philosophy and mathematics. Over time, its formalization into Boolean algebra was accompanied by the recognition that a wide range of combinatorial problems can be expressed as propositional satisfiability (SAT) problems. Because of this dual role, SAT developed into a mature, multi-faceted scientific discipline, and from the earliest days of computing a search was underway to discover how to solve SAT problems in an automated (...) fashion. This book, the Handbook of Satisfiability, is the second, updated and revised edition of the book first published in 2009 under the same name. The handbook aims to capture the full breadth and depth of SAT and to bring together significant progress and advances in automated solving. Topics covered span practical and theoretical research on SAT and its applications and include search algorithms, heuristics, analysis of algorithms, hard instances, randomized formulae, problem encodings, industrial applications, solvers, simplifiers, tools, case studies and empirical results. SAT is interpreted in a broad sense, so as well as propositional satisfiability, there are chapters covering the domain of quantified Boolean formulae (QBF), constraints programming techniques (CSP) for word-level problems and their propositional encoding, and satisfiability modulo theories (SMT). An extensive bibliography completes each chapter. This second edition of the handbook will be of interest to researchers, graduate students, final-year undergraduates, and practitioners using or contributing to SAT, and will provide both an inspiration and a rich resource for their work. Edmund Clarke, 2007 ACM Turing Award Recipient: "SAT solving is a key technology for 21st century computer science." Donald Knuth, 1974 ACM Turing Award Recipient: "SAT is evidently a killer app, because it is key to the solution of so many other problems." Stephen Cook, 1982 ACM Turing Award Recipient: "The SAT problem is at the core of arguably the most fundamental question in computer science: What makes a problem hard?". (shrink)

We consider two‐variable, first‐order logic in which a single distinguished predicate is required to be interpreted as a transitive relation. We show that the finite satisfiability problem for this logic is decidable in triply exponential non‐deterministic time. Complexity falls to doubly exponential non‐deterministic time if the transitive relation is constrained to be a partial order.

Intractability is a growing concern across the cognitive sciences: while many models of cognition can describe and predict human behavior in the lab, it remains unclear how these models can scale to situations of real-world complexity. Cognition and Intractability is the first book to provide an accessible introduction to computational complexity analysis and its application to questions of intractability in cognitive science. Covering both classical and parameterized complexity analysis, it introduces the mathematical concepts and proof techniques that can be (...) used to test one's intuition of tractability. It also describes how these tools can be applied to cognitive modeling to deal with intractability, and its ramifications, in a systematic way. Aimed at students and researchers in philosophy, cognitive neuroscience, psychology, artificial intelligence, and linguistics who want to build a firm understanding of intractability and its implications in their modeling work, it is an ideal resource for teaching or self-study. (shrink)

The Hilbert–Bernays Theorem establishes that for any satisfiable first-order quantificational schema S, one can write out linguistic expressions that are guaranteed to yield a true sentence of elementary arithmetic when they are substituted for the predicate letters in S. The theorem implies that if L is a consistent, fully interpreted language rich enough to express elementary arithmetic, then a schema S is valid if and only if every sentence of L that can be obtained by substituting predicates of L for (...) predicate letters in S is true. The theorem therefore licenses us to define validity substitutionally in languages rich enough to express arithmetic. The heart of the theorem is an arithmetization of Gödel's completeness proof for first-order predicate logic. Hilbert and Bernays were the first to prove that there is such an arithmetization. Kleene established a strengthened version of it, and Kreisel, Mostowski, and Putnam refined Kleene's result. Despite the later refinements, Kleene's presentation of th.. (shrink)

This article explores the practice of simulation modeling by investigating how parameterizations are constructed and integrated into existing frameworks. Parameterizations are simplified process descriptions adapted for simulation models. On the basis of a study of meteorological research, the article presents predictive and representative construction as two different ways of developing parameterizations and the trade-offs involved in this work. Because the overall aim in predictive construction is to improve weather forecasts, the most practical solutions are chosen over the best theoretical solutions. (...) In representative construction, the situation is reversed, but while discourse focuses on theory and models, the everyday work is often tied to computer programs. These different ways of construction work are closely related to the role of the simulation models as epistemic or technical objects, and this characterization is also used to compare the results with previous research. (shrink)

Setting out to understand the effects of positive moral emotions in leadership, this research examines the consequences of leaders’ expressions of gratitude and pride for their followers. In two experimental vignette studies and a field study, leaders’ gratitude expressions showed a positive effect and leaders’ pride expressions showed a negative effect on followers’ ascriptions of leader selfishness. Thereby, leaders’ gratitude expression indirectly led to higher follower satisfaction with and OCB towards the leader, while leaders’ pride expressions indirectly reduced satisfaction with (...) and OCB towards the leader. Furthermore, leaders’ expressions of gratitude indirectly reduced followers’ intentions to leave the leader, while leaders’ expressions of pride indirectly fuelled them. Although ascriptions of selfishness consistently influenced these leader outcomes more strongly than comparable organizational outcomes, results on organizational outcomes were mixed. While leaders’ expressions of gratitude led, as expected, to higher job satisfaction and lower turnover intentions, leaders’ expressions of pride showed positive relations with both OCB towards the organization and intentions to leave the organization. We discuss the theoretical implications of leaders’ expressions of positive moral emotions as signals of outcome attributions, as well as leaders’ selfishness and practical implications that help leaders build followers’ satisfaction and positive leader–follower relationships. (shrink)

In [4] R.Cowen considers a generalization of the resolution rule for hypergraphs and introduces a notion of satisfiability of families of sets of vertices via 2-colorings piercing elements of such families. He shows, for finite hypergraphs with no one-element edges that if the empty set is a consequence ofA by the resolution rule, thenA is not satisfiable. Alas the converse is true for a restricted class of hypergraphs only, and need not to be true in the general case. In (...) this paper we show that weakening slightly the notion of satisfiability, we get the equivalence of unsatisfiability and the derivability of the empty set for any hypergraph. Moreover, we show the compactness property of hypergraph satisfiability and state its equivalence to BPI, i.e. to the statement that in every Boolean algebra there exists an ultrafilter. (shrink)

Hegel had taken the Kantian categories of thought to be merely formal, without content, since, he argued, Kant abstracted the conditions of thought from the world. The Kantian categories can, as such, only be understood subjectively and so are unable to secure a content for themselves. Hegel, following Fichte, tried to provide a content for the logical categories. In order to reinstate an objective status for logic and conceptuality he tries to affirm the unity of thought and being. The idea (...) that this unity is established by reinstating a pre-Kantian metaphysics has in most of the recent Hegel literature been discredited. In the wake of this non-metaphysical Hegel there is a concern that the architectonic of concepts which is taken as the organizing principle of consciousness offers an account of experience which is too schematic. While Hegel disputes the intuition/concept distinction as it is played out in Kant and Fichte, he does nevertheless retain some residue of a notion of intuition in his theory of the Concept. This is central to understanding his notion of experience as it can't simply be equated with rule governed conceptuality. Satisfying the demands of reason for Hegel requires more than conceiving our experience solely as judgments. (shrink)

Spirituality in the workplace is gaining recognition and value among researchers, academicians, and business professionals. The aim of this paper is to examine the impact of spirituality in the workplace on job satisfaction by measuring four dimensions of spirituality in the workplace: meaningful work, sense of community, organizational values, and compassion. The impact of each dimension on job satisfaction is hypothesized. A cross-sectional survey was used to collect data from 100 payroll employees in private insurance companies in Punjab. A correlation (...) analysis showed a positive relationship between all the dimensions of spirituality in the workplace and job satisfaction. A regression analysis revealed that although all the dimensions of spirituality in the workplace are important, organizational values and a sense of community are the most important in terms of the job satisfaction level of employees. This work will help insurance companies to better understand the concept of spirituality in the workplace and its importance. Insurance companies can improve their functioning by encouraging employee spirituality in the workplace. (shrink)

In this paper, we take up the question of whether there comes a point at which one is no longer morally obliged to do further good, even at very low cost to oneself. More specifically, they ask: under precisely what conditions is it plausible to say that that “point” has been reached? A crude account might focus only on, say, the amount of good the agent has already done, but a moment’s reflection shows that this is indeed too crude. We (...) develop and defend a nuanced account according to which considerations of three types are all relevant to whether one has satisfied one’s duties to assist: “inputs” (types and quantities of sacrifice made), “characteristics” (the beliefs and intentions that informed the donor’s decisions), and “success” (the extent to which the donations in question succeeded in generating value). (shrink)

In first order logic without equality, but with arbitrary relations and functions the ∃*∀∃* class is the unique maximal solvable prefix class. We show that the satisfiability problem for this class is decidable in deterministic exponential time The result is established by a structural analysis of a particular infinite subset of the Herbrand universe and by a polynomial space bounded alternating procedure.