Effective Fitness Landscapes for Evolutionary Systems

In evolution theory the concept of a fitness landscape has played an important role, evolution itself being portrayed as a hill-climbing process on a rugged landscape. In this article it is shown that in general, in the presence of other genetic operators such as mutation and recombination, hill-climbing is the exception rather than the rule. This descrepency can be traced to the different ways that the concept of fitness appears --- as a measure of the number of fit offspring, or as a measure of the probability to reach reproductive age. Effective fitness models the former not the latter and gives an intuitive way to understand population dynamics as flows on an effective fitness landscape when genetic operators other than selection play an important role. The efficacy of the concept is shown using several simple analytic examples and also some more complicated cases illustrated by simulations.Comment: 11 pages, 8 postscript figure

Fragments of Frege's Grundgesetze and G\"odel's Constructible Universe

Frege's Grundgesetze was one of the 19th century forerunners to contemporary set theory which was plagued by the Russell paradox. In recent years, it has been shown that subsystems of the Grundgesetze formed by restricting the comprehension schema are consistent. One aim of this paper is to ascertain how much set theory can be developed within these consistent fragments of the Grundgesetze, and our main theorem shows that there is a model of a fragment of the Grundgesetze which defines a model of all the axioms of Zermelo-Fraenkel set theory with the exception of the power set axiom. The proof of this result appeals to G\"odel's constructible universe of sets, which G\"odel famously used to show the relative consistency of the continuum hypothesis. More specifically, our proofs appeal to Kripke and Platek's idea of the projectum within the constructible universe as well as to a weak version of uniformization (which does not involve knowledge of Jensen's fine structure theory). The axioms of the Grundgesetze are examples of abstraction principles, and the other primary aim of this paper is to articulate a sufficient condition for the consistency of abstraction principles with limited amounts of comprehension. As an application, we resolve an analogue of the joint consistency problem in the predicative setting.Comment: Forthcoming in The Journal of Symbolic Logi

Social Structures for Learning

This article investigates what learning groups there are in organizations, other than the familiar 'communities of practice'. It first develops an interdisciplinary theoretical framework for identifying, categorizing and understanding learning groups. For this, it employs a constructivist, interactionist theory of knowledge and learning. It employs elements of transaction cost theory and of social theory of trust. Transaction cost economics neglects learning and trust, but elements of the theory are still useful. The framework is used in an empirical study in a consultancy company, to explore what learning groups there are, and to see if our theory can explain their functioning and their success or failure.learning groups;social theory of trust;theory of knowledge and learning;transaction cost theory

RODI: Benchmarking Relational-to-Ontology Mapping Generation Quality

Accessing and utilizing enterprise or Web data that is scattered across multiple data sources is an important task for both applications and users. Ontology-based data integration, where an ontology mediates between the raw data and its consumers, is a promising approach to facilitate such scenarios. This approach crucially relies on useful mappings to relate the ontology and the data, the latter being typically stored in relational databases. A number of systems to support the construction of such mappings have recently been developed. A generic and effective benchmark for reliable and comparable evaluation of the practical utility of such systems would make an important contribution to the development of ontology-based data integration systems and their application in practice. We have proposed such a benchmark, called RODI. In this paper, we present a new version of RODI, which significantly extends our previous benchmark, and we evaluate various systems with it. RODI includes test scenarios from the domains of scientific conferences, geographical data, and oil and gas exploration. Scenarios are constituted of databases, ontologies, and queries to test expected results. Systems that compute relational-to-ontology mappings can be evaluated using RODI by checking how well they can handle various features of relational schemas and ontologies, and how well the computed mappings work for query answering. Using RODI, we conducted a comprehensive evaluation of seven systems

A Uniform Substitution Calculus for Differential Dynamic Logic

This paper introduces a new proof calculus for differential dynamic logic (dL) that is entirely based on uniform substitution, a proof rule that substitutes a formula for a predicate symbol everywhere. Uniform substitutions make it possible to rely on axioms rather than axiom schemata, substantially simplifying implementations. Instead of nontrivial schema variables and soundness-critical side conditions on the occurrence patterns of variables, the resulting calculus adopts only a finite number of ordinary dL formulas as axioms. The static semantics of differential dynamic logic is captured exclusively in uniform substitutions and bound variable renamings as opposed to being spread in delicate ways across the prover implementation. In addition to sound uniform substitutions, this paper introduces differential forms for differential dynamic logic that make it possible to internalize differential invariants, differential substitutions, and derivations as first-class axioms in dL

On Automating the Doctrine of Double Effect

The doctrine of double effect ($\mathcal{DDE}$) is a long-studied ethical principle that governs when actions that have both positive and negative effects are to be allowed. The goal in this paper is to automate $\mathcal{DDE}$. We briefly present $\mathcal{DDE}$, and use a first-order modal logic, the deontic cognitive event calculus, as our framework to formalize the doctrine. We present formalizations of increasingly stronger versions of the principle, including what is known as the doctrine of triple effect. We then use our framework to simulate successfully scenarios that have been used to test for the presence of the principle in human subjects. Our framework can be used in two different modes: One can use it to build $\mathcal{DDE}$-compliant autonomous systems from scratch, or one can use it to verify that a given AI system is $\mathcal{DDE}$-compliant, by applying a $\mathcal{DDE}$ layer on an existing system or model. For the latter mode, the underlying AI system can be built using any architecture (planners, deep neural networks, bayesian networks, knowledge-representation systems, or a hybrid); as long as the system exposes a few parameters in its model, such verification is possible. The role of the $\mathcal{DDE}$ layer here is akin to a (dynamic or static) software verifier that examines existing software modules. Finally, we end by presenting initial work on how one can apply our $\mathcal{DDE}$ layer to the STRIPS-style planning model, and to a modified POMDP model.This is preliminary work to illustrate the feasibility of the second mode, and we hope that our initial sketches can be useful for other researchers in incorporating DDE in their own frameworks.Comment: 26th International Joint Conference on Artificial Intelligence 2017; Special Track on AI & Autonom

Combining Exploratory Learning With Structured Practice to Foster Conceptual and Procedural Fractions Knowledge

Robust domain knowledge consists of conceptual and procedural knowledge. The two types of knowledge develop together, but are fostered by different learning tasks. Exploratory tasks enable students to manipulate representations and discover the underlying concepts. Structured tasks let students practice problem-solving procedures step-by-step. Educational technology has mostly relied on providing only either task type, with a majority of learning environments focusing on structured tasks. We investigated in two quasi-experimental studies with 8-10 years old students from UK (N = 121) and 10-12 years old students from Germany (N = 151) whether a combination of both task types fosters robust knowledge more than structured tasks alone. Results confirmed this hypothesis and indicate that students learning with a combination of tasks gained more conceptual knowledge and equal procedural knowledge compared to students learning with structured tasks only. The results illustrate the efficacy of combining both task types for fostering robust fractions knowledge

Uniform Substitution for Differential Game Logic

This paper presents a uniform substitution calculus for differential game logic (dGL). Church's uniform substitutions substitute a term or formula for a function or predicate symbol everywhere. After generalizing them to differential game logic and allowing for the substitution of hybrid games for game symbols, uniform substitutions make it possible to only use axioms instead of axiom schemata, thereby substantially simplifying implementations. Instead of subtle schema variables and soundness-critical side conditions on the occurrence patterns of logical variables to restrict infinitely many axiom schema instances to sound ones, the resulting axiomatization adopts only a finite number of ordinary dGL formulas as axioms, which uniform substitutions instantiate soundly. This paper proves soundness and completeness of uniform substitutions for the monotone modal logic dGL. The resulting axiomatization admits a straightforward modular implementation of dGL in theorem provers

Valentine: Evaluating Matching Techniques for Dataset Discovery

Data scientists today search large data lakes to discover and integrate datasets. In order to bring together disparate data sources, dataset discovery methods rely on some form of schema matching: the process of establishing correspondences between datasets. Traditionally, schema matching has been used to find matching pairs of columns between a source and a target schema. However, the use of schema matching in dataset discovery methods differs from its original use. Nowadays schema matching serves as a building block for indicating and ranking inter-dataset relationships. Surprisingly, although a discovery method's success relies highly on the quality of the underlying matching algorithms, the latest discovery methods employ existing schema matching algorithms in an ad-hoc fashion due to the lack of openly-available datasets with ground truth, reference method implementations, and evaluation metrics. In this paper, we aim to rectify the problem of evaluating the effectiveness and efficiency of schema matching methods for the specific needs of dataset discovery. To this end, we propose Valentine, an extensible open-source experiment suite to execute and organize large-scale automated matching experiments on tabular data. Valentine includes implementations of seminal schema matching methods that we either implemented from scratch (due to absence of open source code) or imported from open repositories. The contributions of Valentine are: i) the definition of four schema matching scenarios as encountered in dataset discovery methods, ii) a principled dataset fabrication process tailored to the scope of dataset discovery methods and iii) the most comprehensive evaluation of schema matching techniques to date, offering insight on the strengths and weaknesses of existing techniques, that can serve as a guide for employing schema matching in future dataset discovery methods