The unprovability of small inconsistency

Summary We show that a consistent, finitely axiomatized, sequential theory cannot prove its own inconsistency on every definable cut. A corollary is that there are at least three degrees of global interpretability of theories equivalent modulo local interpretability to a consistent, finitely axiomatized, sequential theory U.     

The complete finitely axiomatized theories of order are dense

We prove a conjecture of Lauchli and Leonard that every sentence of the theory of linear order which has a model, has a model with a finitely axiomatized theory.     

Binary interactions and subset choice

Subset evaluation and choice problems abound in practical decision settings. They are often analyzed with linear objective functions that value subsets as sums of utilities of items in the subsets. This simplifies assessment and computational tasks but runs a risk of substantial suboptimality because it disregards evaluative interdependencies among items.This paper examines a binary-interaction model that accounts for preference interdependencies between items. Ordinal and cardinal versions of the model are axiomatized and compared to the simpler linear model as well as the general model that incorporates all orders of interdependence. Comparisons of computational complexity for standard subset-choice problems are made between the linear and binary-interaction models.     

Interpretability degrees of finitely axiomatized sequential theories

In this paper we show that the degrees of interpretability of finitely axiomatized extensions-in-the-same-language of a finitely axiomatized sequential theory—like Elementary Arithmetic EA, IΣ₁, or the Gödel–Bernays theory of sets and classes GB—have suprema. This partially answers a question posed by ?vejdar in his paper (Commentationes Mathematicae Universitatis Carolinae 19:789–813, 1978). The partial solution of ?vejdar’s problem follows from a stronger fact: the convexity of the degree structure of finitely axiomatized extensions-in-the-same-language of a finitely axiomatized sequential theory in the degree structure of the degrees of all finitely axiomatized sequential theories. In the paper we also study a related question: the comparison of structures for interpretability and derivability. In how far can derivability mimic interpretability? We provide two positive results and one negative result.     

Combined stress and human performance: a weighted digraph model

Weighted directed graphs are described and offered as possible aids to the analysis of the interactive effects of multiple independent variables on human behavior. Examples in which weighted digraphs represent the interactions among multiple stressors and performance indices are presented, and pulse process analysis is used to derive empirical predictions from the models.     

On extensions of Nelson’s logic satisfying Dummett’s axiom

The class of extensions is completely described of the logic obtained by adding Dummett’s axiom to the paraconsistent Nelson logic. Moreover, we prove that every extension of this logic is finitely axiomatizable and decidable and, given a formula, it is possible to determine which extension is axiomatized by this formula.     

Comparing multi-dimensional contingency fit to financial performance of organizations

In theory, it is widely accepted that an organization’s optimal structure is contingent upon various situational factors such as market conditions, nature of work and properties of technology. In practice, providing practical advice based on this understanding has been difficult. This paper demonstrates that it is possible to find a correlation between financial performance, as measured by growth in Return on Assets, and degree of compliance with the recommendations of the contingency theory model known as Interaction Value Analysis (IVA). IVA is based on an abstract theoretical representation of organizational work as a series of value-adding interactions among rational value-maximizing agents. Six different dimensions of an organization’s situation are represented as parameters of the equation that sums up the value added by all interactions within the organization. This “Multi-dimensional” approach is contrasted with the “Multi-contingency” model, which aggregates the effects of multiple contingent-design rules without considering how the rules overlap or otherwise influence one another. The success of the six-parameter IVA model in partially predicting financial performance is an inducement to expand IVA to include more of the parameters included in the Multi-contingency model.     

Going Beyond the Data: Empirical Validation Leading to Grounded Theory

The purpose of this study is two-fold. First, a validation study on Construct-TM is conducted to show that modeling the actual and cognitive knowledge networks of a group can produce agent interactions within the model that correlate significantly with the communication network obtained from empirical data. Second, empirically grounded theory is produced by combining empirical data with simulation experiments run on empirically validated models.     

Kripke submodels and universal sentences

We define two notions for intuitionistic predicate logic: that of a submodel of a Kripke model, and that of a universal sentence. We then prove a corresponding preservation theorem. If a Kripke model is viewed as a functor from a small category to the category of all classical models with (homo)morphisms between them, then we define a submodel of a Kripke model to be a restriction of the original Kripke model to a subcategory of its domain, where every node in the subcategory is mapped to a classical submodel of the corresponding classical model in the range of the original Kripke model. We call a sentence universal if it is built inductively from atoms (including ? and ⊥) using ∧, ∨, ?, and →, with the restriction that antecedents of → must be atomic. We prove that an intuitionistic theory is axiomatized by universal sentences if and only if it is preserved under Kripke submodels. We also prove the following analogue of a classical model‐consistency theorem: The universal fragment of a theory Γ is contained in the universal fragment of a theory Δ if and only if every rooted Kripke model of Δ is strongly equivalent to a submodel of a rooted Kripke model of Γ. Our notions of Kripke submodel and universal sentence are natural in the sense that in the presence of the rule of excluded middle, they collapse to the classical notions of submodel and universal sentence. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Associated consistency and values for TU games

In the framework of the solution theory for cooperative transferable utility games, Hamiache axiomatized the well-known Shapley value as the unique one-point solution verifying the inessential game property, continuity, and associated consistency. The purpose of this paper is to extend Hamiache’s axiomatization to the class of efficient, symmetric, and linear values, of which the Shapley value is the most important representative. For this enlarged class of values, explicit relationships to the Shapley value are exploited in order to axiomatize such values with reference to a slightly adapted inessential game property, continuity, and a similar associated consistency. The latter axiom requires that the solutions of the initial game and its associated game (with the same player set, but a different characteristic function) coincide.     

Intra-party decision making, party formation, and moderation in multiparty systems

We establish coalitional stable party structures of a party formation game in an elected assembly. Farsighted political players can commit to form parties and to vote on policies according to the party position which is determined by intra-party majority rule. Parties may form governments and block proposals by a randomly selected member of the government. If the government recognition rule allows for the formation of multiparty governments, the median parliamentarian either realizes her ideal point or a policy lottery which she strictly prefers to the status quo. This outcome is enforced by the threat of forming a moderating centre party.     

Anonymity and one-way authentication in key exchange protocols

Key establishment is a crucial cryptographic primitive for building secure communication channels between two parties in a network. It has been studied extensively in theory and widely deployed in practice. In the research literature a typical protocol in the public-key setting aims for key secrecy and mutual authentication. However, there are many important practical scenarios where mutual authentication is undesirable, such as in anonymity networks like Tor, or is difficult to achieve due to insufficient public-key infrastructure at the user level, as is the case on the Internet today. In this work we are concerned with the scenario where two parties establish a private shared session key, but only one party authenticates to the other; in fact, the unauthenticated party may wish to have strong anonymity guarantees. We present a desirable set of security, authentication, and anonymity goals for this setting and develop a model which captures these properties. Our approach allows for clients to choose among different levels of authentication. We also describe an attack on a previous protocol of Øverlier and Syverson, and present a new, efficient key exchange protocol that provides one-way authentication and anonymity.     

Why modelling and model use matter

When OR/MS analysts develop a model, how are they intending this model to be used? There are many different ways in which OR/MS models may be classified and one important categorisation is the intended use of the model. Some models are intended for routine use on a frequent basis, with little or no human intervention. Others form part of human decision process and provide support to that process. Considering model validation, data requirements, added value and possible pitfalls leads to a theory of model use based on four categories: decision automation, routine decision support, investigation and improvement, and generating insights for debate. A pilot investigation in an OR/MS group demonstrates that this categorisation could provide the basis for empirical research into a theory of model use in operational research. A theory of model use would be of value to academics, who could prioritise their work, and to practitioners, who could place their own work in a broader landscape.     

Faith & falsity

A theory T is trustworthy iff, whenever a theory U is interpretable in T, then it is faithfully interpretable. In this paper we give a characterization of trustworthiness. We provide a simple proof of Friedman’s Theorem that finitely axiomatized, sequential, consistent theories are trustworthy. We provide an example of a theory whose schematic predicate logic is complete Π₂⁰.     

Sequence encoding without induction

We show that the universally axiomatized, induction‐free theory $\mathsf {PA}^-$ is a sequential theory in the sense of Pudlák's 5 , in contrast to the closely related Robinson's arithmetic.     

On the cobordism and commutative monoid with cancellation approaches to conformal field theory

In the late 1980s, Graeme Segal axiomatized conformal field theory in terms of a cobordism category. In that same preprint he outlined a more symmetric trace approach, which was recently rigorized in terms of pseudo algebras over a 2-theory. In this paper, we treat the cobordism approach in the pseudo algebra context. We introduce a new algebraic structure on a bicategory, called a pseudo 2-algebra over a theory, as a means of comparison for the two approaches. The main result states that the 2-category of pseudo algebras over a fixed 2-theory is biequivalent to the 2-category of pseudo 2-algebras over a fixed theory in certain situations.     

Government formation in a two dimensional policy space

Given any allocation of parliament seats among parties, we characterize all the stable government configurations (supported by at least a majority of the parliament) in terms of winning coalitions and policy outcomes. We consider a two dimensional policy space and we assume that there are four parties that care mainly about holding office, and only instrumentally about policy. We find that for any distribution of seats in the parliament only two scenarios are possible: either there is a party that is a member of almost all equilibrium coalitions (dominant party scenario) or there is a party that is never a member of an equilibrium coalition (dominated party scenario). We characterize the key party for each possible scenario and we show that it is sufficient that the key party has intense preferences over one the issues to guarantee the formation of a stable government coalition.     

Axiomatizing Provable <Emphasis Type="Italic">n</Emphasis>-Provability

The set of all formulas whose n-provability in a given arithmetical theory S is provable in another arithmetical theory T is a recursively enumerable extension of S. We prove that such extensions can be naturally axiomatized in terms of transfinite progressions of iterated local reflection schemata over S. Specifically, the set of all provably 1-provable sentences in Peano arithmetic PA can be axiomatized by an ε₀-times iterated local reflection schema over PA. The resulting characterizations provide additional information on the proof-theoretic strength of these theories and on the complexity of their axiomatization.     

Multivariate negative binomial models for insurance claim counts

It is no longer uncommon these days to find the need in actuarial practice to model claim counts from multiple types of coverage, such as the ratemaking process for bundled insurance contracts. Since different types of claims are conceivably correlated with each other, the multivariate count regression models that emphasize the dependency among claim types are more helpful for inference and prediction purposes. Motivated by the characteristics of an insurance dataset, we investigate alternative approaches to constructing multivariate count models based on the negative binomial distribution. A classical approach to induce correlation is to employ common shock variables. However, this formulation relies on the NB-I distribution which is restrictive for dispersion modeling. To address these issues, we consider two different methods of modeling multivariate claim counts using copulas. The first one works with the discrete count data directly using a mixture of max-id copulas that allows for flexible pair-wise association as well as tail and global dependence. The second one employs elliptical copulas to join continuitized data while preserving the dependence structure of the original counts. The empirical analysis examines a portfolio of auto insurance policies from a Singapore insurer where claim frequency of three types of claims (third party property damage, own damage, and third party bodily injury) are considered. The results demonstrate the superiority of the copula-based approaches over the common shock model. Finally, we implemented the various models in loss predictive applications.