. 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)

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)

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.

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

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)

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)

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 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)

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)

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.

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)

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)

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)

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)

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)

Under the normal assumptions of quantum field theory, Haag’s theorem states that any field unitarily equivalent to a free field must itself be a free field. Unfortunately, the derivation of the Dyson series perturbation expansion relies on the use of the interaction picture, in which the interacting field is unitarily equivalent to the free field but must still account for interactions. Thus, the traditional perturbative derivation of the scattering matrix in quantum field theory is mathematically ill defined. Nevertheless, perturbative quantum (...) field theory is currently the only practical approach for addressing scattering for realistic interactions, and it has been spectacularly successful in making empirical predictions. This paper explains this success by showing that Haag’s Theorem can be avoided when quantum field theory is formulated using an invariant, fifth path parameter in addition to the usual four position parameters, such that the Dyson perturbation expansion for the scattering matrix can still be reproduced. As a result, the parameterized formalism provides a consistent foundation for the interpretation of quantum field theory as used in practice and, perhaps, for better dealing with other mathematical issues. (shrink)

Given someone’s fully specified posterior probability distribution q and information about the revision method that they employed to produce q, what can you infer about their prior probabilistic commitments? This question provides an entrée into a thoroughgoing discussion of a class of parameterizations of Jeffrey conditioning in which the parameters furnish information above and beyond that incorporated in \. Our analysis highlights the ubiquity of Bayes factors in the study of probability revision.

We prove, by explicit construction, that not all sets definable in polynomially bounded o-minimal structures have mild parameterization. Our methods do not depend on the bounds particular to the definition of mildness and therefore our construction is also valid for a generalized form of parameterization, which we call G-mild. Moreover, we present a cell decomposition result for certain o-minimal structures which may be of independent interest. This allows us to show how our construction can produce polynomially bounded, model (...) complete expansions of the real ordered field which, in addition to lacking G-mild parameterization, nonetheless still have analytic cell decomposition. (shrink)

Relatively congruence regular quasivarieties and quasivarieties of logic have noticeable similarities. The paper provides a unifying framework for them which extends the Blok-Pigozzi theory of elementarily algebraizable (and protoalgebraic) deductive systems. In this extension there are two parameters: a set of terms and a variable. When the former is empty or consists of theorems, the Blok-Pigozzi theory is recovered, and the variable is redundant. On the other hand, a class of membership logics is obtained when the variable is the only (...) element of the set of terms. For these systems the appropriate variant of equivalent algebraic semantics encompasses the relatively congruence regular quasivarieties. (shrink)

Relatively congruence regular quasivarieties and quasivarieties of logic have noticeable similarities. The paper provides a unifying framework for them which extends the Blok-Pigozzi theory of elementarily algebraizable (and protoalgebraic) deductive systems. In this extension there are two parameters: a set of terms and a variable. When the former is empty or consists of theorems, the Blok-Pigozzi theory is recovered, and the variable is redundant. On the other hand, a class of ‘membership logics’ is obtained when the variable is the only (...) element of the set of terms. For these systems the appropriate variant of equivalent algebraic semantics encompasses the relatively congruence regular quasivarieties. (shrink)

In explaining the reasons for sustained existence of tolerance in Indian philosophical mind and continuation of tolerant practices in socio-political life, Amartya Sen argues that tolerance is inherently a social enterprise, which may appear as contingent, but for all intents and purposes is persistent. Basing his thesis that is opposed to Cartesian dualism, which makes a distinction between mind and body, Sen submits that Indian system of universalizing perception finds a subtle form of connection between mind and body. He expands (...) the ancient core worldview, Vasundhara kutumbakam as a secular tolerant civil code,1which makes a connection between the transcendental and the pragmatic planes of consciousness, and reconstructs a thesis about tolerance around human consciousness, which is collectivized and anchored in an acknowledged public space in society that is joined together psychologically as well as philosophically. Tolerance as consciousness can be regarded a necessary condition for playing the role of intentionality as stipulated by classical philosophy. Aware of this ancient wisdom that accepts relativism as an impasse over some evaluative matter, Sen avoids the pitfalls of cultural relativism in tolerance by offering an argument that is based on the metaphysics of Advaita Vedanta and other religious and secular literature, and epitomizes an internationalizing virtue in tolerant traditions. I would examine some interconnected issues, such as the ethical “perimeter” of Sen’s philosophical observation of totalized value system and Indian tolerant attitudes in real life, etc., raising the broader question about the location of cultural identity in relation to supranational state organization. My chief argument is that Sen has been able to observe a connection between the Advaita Vedantic moral philosophy that informs that viewed from the Brahmanic perspective of absolute knowledge in unity, the apparent subject of duality is not the ultimate subject. My conclusion is that valuing of tolerance, individual liberty as well as civil rights is a particular contribution of Western thinking and philosophy; the Western advocates of these rights often provide ammunition to the non-Western critics of tolerance and human rights. (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)

We use a result due to Rolin, Speissegger, and Wilkie to show that definable sets in certain o-minimal structures admit definable parameterizations by mild maps. We then use this parameterization to prove a result on the density of rational points on curves defined by restricted Pfaffian functions.

We investigate the index sets associated with the degree structures of computable sets under the parameterized reducibilities introduced by the authors. We solve a question of Peter Cholakand the first author by proving the fundamental index sets associated with a computable set A, {e : W e ≤ q u A} for q∈ {m, T} are Σ4 0 complete. We also show hat FPT(≤ q n ), that is {e : W e computable and ≡ q n ?}, is Σ4 (...) 0 complete. We also look at computable presentability of these classes. (shrink)

We show that Bell inequalities can be violated in the macroscopic world. The macroworld violation is illustrated using an example involving connected vessels of water. We show that whether the violation of inequalities occurs in the microworld or the macroworld, it is the identification of nonidentical events that plays a crucial role. Specifically, we prove that if nonidentical events are consistently differentiated, Bell-type Pitowsky inequalities are no longer violated, even for Bohm's example of two entangled spin 1/2 quantum particles. We (...) show how Bell inequalities can be violated in cognition, specifically in the relationship between abstract concepts and specific instances of these concepts. This supports the hypothesis that genuine quantum structure exists in the mind. We introduce a model where the amount of nonlocality and the degree of quantum uncertainty are parameterized, and demonstrate that increasing nonlocality increases the degree of violation, while increasing quantum uncertainty decreases the degree of violation. (shrink)

Psychologists and philosophers have recently been exploring whether the mechanisms which underlie the acquisition of ‘theory of mind’ (ToM) are best charac- terized as cognitive modules or as developing theories. In this paper, we attempt to clarify what a modular account of ToM entails, and why it is an attractive type of explanation. Intuitions and arguments in this debate often turn on the role of develop- ment: traditional research on ToM focuses on various developmental sequences, whereas cognitive modules are thought (...) to be static and ‘anti-developmental’. We suggest that this mistaken view relies on an overly limited notion of modularity, and we explore how ToM might be grounded in a cognitive module and yet still afford development. Modules must ‘come on-line’, and even fully developed modules may still develop internally, based on their constrained input. We make these points con- crete by focusing on a recent proposal to capture the development of ToM in a module via parameterization. (shrink)

Cognitive science has been beset for thirty years by foundational disputes about the nature and extension of cognition—e.g. whether cognition is necessarily representational, whether cognitive processes extend outside the brain or body, and whether plants or microbes have them. Whereas previous philosophical work aimed to settle these disputes, I aim to understand what conception of cognition scientists could share given that they disagree so fundamentally. To this end, I develop a number of variations on traditional conceptual explication, and defend a (...) novel explication of cognition called the sensitive management hypothesis. -/- Since expert judgments about the extension of “cognition” vary so much, I argue that there is value in explication that accurately models the variance in judgments rather than taking sides or treating that variance as noise. I say of explications that accomplish this that they are ecumenically extensionally adequate. Thus, rather than adjudicating whether, say, plants can have cognitive processes like humans, an ecumenically adequate explication should classify these cases differently: human cognitive processes as paradigmatically cognitive, and plant processes as controversially cognitive. -/- I achieve ecumenical adequacy by articulating conceptual explications with parameters, or terms that can be assigned a number of distinct interpretations based on the background commitments of participants in a discourse. For example, an explication might require that cognition cause “behavior,” and imply that plant processes are cognitive or not depending on whether anything plants do can be considered “behavior.” Parameterization provides a unified treatment of embattled concepts by isolating topics of disagreement in a small number of parameters. -/- I incorporate these innovations into an account on which cognition is the “sensitive management of organismal behavior.” The sensitive management hypothesis is ecumenically extensionally adequate, accurately classifying a broad variety of cases as paradigmatically or controversially cognitive phenomena. I also describe an extremely permissive version of the sensitive management hypothesis, arguing that it has the potential to explain several features of cognitive scientific discourse, including various facts about the way cognitive scientists ascribe representations to cognitive systems. (shrink)

Drawing on different suggestions from the literature, we outline a unified metaphysical framework, labeled as Modal Meinongian Metaphysics (MMM), combining Meinongian themes with a non-standard modal ontology. The MMM approach is based on (1) a comprehension principle (CP) for objects in unrestricted, but qualified form, and (2) the employment of an ontology of impossible worlds, besides possible ones. In §§1–2, we introduce the classical Meinongian metaphysics and consider two famous Russellian criticisms, namely (a) the charge of inconsistency and (b) the (...) claim that naïve Meinongianism allows one to prove that anything exists. In §3, we have impossible worlds enter the stage and provide independent justification for their use. In §4, we introduce our revised comprehension principle: our CP has no restriction on the (sets of) properties that can characterize objects, but parameterizes them to worlds, therefore having modality explicitly built into it. In §5, we propose an application of the MMM apparatus to fictional objects and defend the naturalness of our treatment against alternative approaches. Finally, in §6, we consider David Lewis’ notorious objection to impossibilia, and provide a reply to it by resorting to an ersatz account of worlds. (shrink)