Logic Journal of IGPL - Advance Access

Extending the Hegselmann-Krause Model I

Douven, I., Riegler, A. — Wed, 18 Nov 2009 23:11:13 PST

Hegselmann and Krause have developed a simple yet powerful computational model for studying the opinion dynamics in societies of epistemically interacting truth-seeking agents. We present various extensions of this model and show their relevance to the investigation of socio-epistemic questions, with an emphasis on normative questions.

Standards and the distribution of cognitive labour: A model of the dynamics of scientific activity

De Langhe, R., Greiff, M. — Wed, 18 Nov 2009 23:11:12 PST

We present a model of the distribution of labour in science. Such models tend to rely on the mechanism of the invisible hand (e.g. Hull 1988, Goldman & Shaked 1991 and Kitcher 1990). Our analysis starts from the necessity of standards in distributed processes and the possibility of multiple standards in science. Invisible hand models turn out to have only limited scope because they are restricted to describing the atypical single-standard case. Our model is a generalisation of these models to J standards; single-standard models such as Kitcher (1990) are a limiting case. We introduce and formalise this model, demonstrate its dynamics and conclude that the conclusions commonly derived from invisible hand models about the distribution of labour in science are not robust against changes in the number of standards.

The weight of competence under a realistic loss function

Hartmann, S., Sprenger, J. — Thu, 12 Nov 2009 04:32:05 PST

In many scientific, economic and policy-related problems, pieces of information from different sources have to be aggregated. Typically, the sources are not equally competent. This raises the question of how the relative weights and competences should be related to arrive at an optimal final verdict. Our paper addresses this question undera more realistic perspective of measuring the practical loss implied by an inaccurate verdict.

Combining totalitarian and Ceteris Paribus semantics in database preference queries

Neves, R. d. S., Kaci, S. — Fri, 06 Nov 2009 01:26:57 PST

Preference queries from databases aim to retrieve the best answers w.r.t. user's requirements. The integration of preferences in database queries has known many advances in the last decade. Most of works however are based on comparative preference statements obeying more or less strong semantics. Representing and reasoning about comparative preference statements has also been widely investigated in Artificial Intelligence. In this paper, we bridge the two frameworks and develop a simple and unified framework to reason about preferences in database queries. Our framework is based on insights from non-monotonic reasoning.

A symbolic/subsymbolic interface protocol for cognitive modeling

Simen, P., Polk, T. — Fri, 30 Oct 2009 06:25:40 PDT

Researchers studying complex cognition have grown increasingly interested in mapping symbolic cognitive architectures onto subsymbolic brain models. Such a mapping seems essential for understanding cognition under all but the most extreme viewpoints (namely, that cognition consists exclusively of digitally implemented rules; or instead, involves no rules whatsoever). Making this mapping reduces to specifying an interface between symbolic and subsymbolic descriptions of brain activity. To that end, we propose parameterization techniques for building cognitive models as programmable, structured, recurrent neural networks. Feedback strength in these models determines whether their components implement classically subsymbolic neural network functions (e.g., pattern recognition), or instead, logical rules and digital memory. These techniques support the implementation of limited production systems. Though inherently sequential and symbolic, these neural production systems can exploit principles of parallel, analog processing from decision-making models in psychology and neuroscience to explain the effects of brain damage on problem solving behavior.

Intuitionistic Propositional Logic with Galois Connections

Dzik, W., Jarvinen, J., Kondo, M. — Tue, 20 Oct 2009 22:44:07 PDT

In this work, an intuitionistic propositional logic with a Galois connection (IntGC) is introduced. In addition to the intuitionistic logic axioms and inference rule of modus ponens, the logic contains only two rules of inference mimicking the performance of Galois connections. Both Kripke-style and algebraic semantics are presented for IntGC, and IntGC is proved to be complete with respect to both of these semantics. We show that IntGC has the finite model property and is decidable, but Glivenko's Theorem does not hold. Duality between algebraic and Kripke semantics is presented, and a representation theorem for Heyting algebras with Galois connections is proved. In addition, an application to rough L-valued sets is presented.

Generalized Davis-Putnam and satisfiability problems in mathematics

Cowen, R. — Fri, 18 Sep 2009 22:27:38 PDT

The well-known Davis-Putnam Procedure used to decide the Sat Problem in Logic is shown to be combinatorial in nature and thus directly applicable to solving various Mathematical "Satisfiability" Problems.

Capturing dynamic conceptual frames

Urbaniak, R. — Fri, 18 Sep 2009 22:27:37 PDT

The main focus of this paper is to develop an adaptive formal apparatus capable of capturing (certain types of) reasoning conducted within the framework of the so-called dynamic conceptual frames. I first explain one of the most recent theories of concepts developed by cognitivists, in which a crucial part is played by the notion of a dynamic frame. Next, I describe how a dynamic frame may be captured by a finite set of first-order formulas and how a formalized adaptive framework for reasoning within a dynamic frame can be developed.

Semantic learning in autonomously active recurrent neural networks

Gros, C., Kaczor, G. — Mon, 14 Sep 2009 23:30:52 PDT

The human brain is autonomously active, being characterized by a self-sustained neural activity which would be present even in the absence of external sensory stimuli. Here we study the interrelation between the self-sustained activity in autonomously active recurrent neural nets and external sensory stimuli.

There is no a priori semantical relation between the influx of external stimuli and the patterns generated internally by the autonomous and ongoing brain dynamics. The question then arises when and how are semantic correlations between internal and external dynamical processes learned and built up?

We study this problem within the paradigm of transient state dynamics for the neural activity in recurrent neural nets, i.e. for an autonomous neural activity characterized by an infinite time-series of transiently stable attractor states. We propose that external stimuli will be relevant during the sensitive periods, viz the transition period between one transient state and the subsequent semi-stable attractor. A diffusive learning signal is generated unsupervised whenever the stimulus influences the internal dynamics qualitatively.

For testing we have presented to the model system stimuli corresponding to the bars and stripes problem. We found that the system performs a non-linear independent component analysis on its own, being continuously and autonomously active. This emergent cognitive capability results here from a general principle for the neural dynamics, the competition between neural ensembles.

A complete axiom set for Hansson's deontic logic DSDL2

Parent, X. — Wed, 09 Sep 2009 03:35:51 PDT

The main contribution of this paper is a (strong) completeness result for an axiomatization of Hansson [13]'s deontic system DSDL2, whose semantics involves a non-necessarily transitive betterness relation. Reference is made to a deductive system put forth by Åqvist [2, 3].

Recurrent policy gradients

Wierstra, D., Forster, A., Peters, J., Schmidhuber, J. — Wed, 09 Sep 2009 03:35:51 PDT

Reinforcement learning for partially observable Markov decision problems (POMDPs) is a challenge as it requires policies with an internal state. Traditional approaches suffer significantly from this shortcoming and usually make strong assumptions on the problem domain such as perfect system models, state-estimators and a Markovian hidden system. Recurrent neural networks (RNNs) offer a natural framework for dealing with policy learning using hidden state and require only few limiting assumptions. As they can be trained well using gradient descent, they are suited for policy gradient approaches.

In this paper, we present a policy gradient method, the Recurrent Policy Gradient which constitutes a model-free reinforcement learning method. It is aimed at training limited-memory stochastic policies on problems which require long-term memories of past observations. The approach involves approximating a policy gradient for a recurrent neural network by backpropagating return-weighted characteristic eligibilities through time. Using a ‘‘Long Short-Term Memory’’ RNN architecture, we are able to outperform previous RL methods on three important benchmark tasks. Furthermore, we show that using history-dependent baselines helps reducing estimation variance significantly, thus enabling our approach to tackle more challenging, highly stochastic environments.

On the directional Lambek calculus

Zielonka, W. — Wed, 09 Sep 2009 03:35:50 PDT

The article presents a calculus of syntactic types which differs from the calculi L and NL of J. Lambek in that, in its Gentzen-like form, sequent antecedents are neither strings (as in L) nor phrase structures (as in NL) but functor-argument structures. The product-free part of the calculus is shown to be equivalent to the system AB due to Ajdukiewicz and Bar-Hillel. However, if the empty sequent antecedent is admitted, the resulting product-free calculus is not finitely cut-rule axiomatizable.

The role of goals in belief selection

Boella, G., da Costa Pereira, C., Pigozzi, G., Tettamanzi, A., van der Torre, L. — Wed, 09 Sep 2009 03:35:50 PDT

In this paper we consider the relation between beliefs and goals in agent theory. Beliefs play three roles in reasoning about goals: they play a role in the generation of unconditional desires from conditional ones, they play a role in adoption of desires as goals, and they play a role in the selection of plans to achieve goals. In this paper we consider the role of goals in reasoning about beliefs. Though we assume that goals do not play a role in the belief generation problem, we argue that they play a role in the belief selection problem. We show the rationality of the use of goals in belief selection, in the sense that there are cases in which agents that take their goals into account in selecting a belief set from a set of alternatives outperform agents that do not do so. We also formally distinguish between the rational role of goals in belief selection and irrational wishful thinking.

Logics of Kripke meta-models

Babenyshev, S., Rybakov, V. — Thu, 03 Sep 2009 03:07:46 PDT

This paper introduces and studies a new type of logical construction, which allows to combine various non-classical propositional logics with the temporal or modal background. The possible candidates include (but are not restricted to) a number of epistemic, multi-agent, deontological and other well-studied logics. In this construction, that we call refinement, the Kripke structure of a chosen Kripke complete logic is imposed on clusters of the background transitive frame. Refinements fit in a wider framework of fibred logics, while having some unique features. First of all, when applied to classes of frames of Kripke complete logics, refinement preserves good meta-logical properties of constituent logics, in contrast with the well-known products of logics. Another advantage of refinements is that they allow for augmented languages of considerable expressive power, while preserving good meta-logical and semantical properties. In particular we show that refinement of logics preserves the effective finite model property and decidability for a wide class of constituent logics.

Reservoir optimization in recurrent neural networks using properties of Kronecker product

Rad, A. A., Hasler, M., Jalili, M. — Thu, 03 Sep 2009 03:07:46 PDT

Recurrent neural networks based on reservoir computing are increasingly being used in many applications. Optimization of the topological structure of the reservoir and the internal connection weights for a given task is one of the most important problems in reservoir computing. In this paper, considering the fact that one can construct a large matrix using Kronecker products of several small-size matrices, we propose a method to optimize the reservoir. Having a small number of parameters to optimize, a gradient based algorithm is applied to optimize parameters, and consequently the reservoir. In addition to reducing the number of parameters for optimization, potentially, the method is able to control several other properties of the reservoir such as spectral radius, sparsity, weight distribution and underlying connections, i.e. connection topology. To reveal the effectiveness of the proposed optimization method, the application to the following tasks are considered: Nonlinear autoregressive moving average and multiple superimposed oscillators. Simulation results show satisfactory performance of the method.

Structure optimization of reservoir networks

Roeschies, B., Igel, C. — Thu, 03 Sep 2009 01:47:29 PDT

Reservoir computing originally relies on a random, fixed population of recurrently connected neurons, but in practice there is a need for algorithms that tailor this reservoir to problem classes. We propose an evolutionary algorithm to adapt size and topology of the network as well as synaptic strengths of connections within the reservoir. Experiments show that the evolved networks significantly outperform standard architectures in terms of prediction performance and compare well with the results of alternative neuroevolution approaches. For applications in which both space and execution time complexity are important, we present an evolutionary multi-objective algorithm addressing the trade-off between identifying dynamical systems with maximum accuracy and minimizing reservoir complexity. This vector optimization algorithm utilizes the contributed hypervolume for selection and for online adaptation of operator probabilities, which considerably improves the search process. Analysis of the evolved networks reveals insights about task-dependent macroscopic properties of the adapted reservoirs.

On vague notions and modalities: a modular approach

Thu, 03 Sep 2009 01:47:29 PDT

Vague notions, such as ‘generally’, ‘rarely’, ‘often’, ‘almost always’, ‘a meaningful subset of a whole’, ‘most’, etc., occur often in ordinary language and in some branches of science. We introduce modal logical systems, with generalized operators, for the precise treatment of assertions involving some versions of such vague notions. We examine modal logics, constructed in a modular fashion, with generalized operators corresponding to some versions of ‘generally’ and ‘rarely’.

Problem of restricted interpolation in superintuitionistic and some modal logics

Maksimova, L. — Fri, 28 Aug 2009 22:47:47 PDT

A restricted interpolation property IPR is investigated in modal and superintuitionistic logics. The problem of description of logics with IPR over the intuitionistic logic Int and the modal Grzegorczyk logic Grz is solved. It is proved that in extensions of Int or Grz IPR is equivalent to the projective Beth property PB2. It follows that IPR is decidable over Int and strongly decidable over Grz.

Perspectives and challenges for recurrent neural network training

Gori, M., Hammer, B., Hitzler, P., Palm, G. — Wed, 26 Aug 2009 07:50:57 PDT

Ontology-revision operators based on reinterpretation

Eschenbach, C., Ozcep, O. L. — Wed, 12 Aug 2009 04:41:30 PDT

Communication between natural or artificial agents relies on the use of a common vocabulary. Since sharing terms does not necessarily imply that the terms have exactly the same meanings for all agents, integrating (trigger) statements into a formal ontology requires mechanisms for resolving conflicts that are caused by the ambiguity of terms specified in different but similar ontologies.

We define and analyze a family of ontology-revision operators that resolve conflicts by disambiguating concept symbols occurring in both the ontology and the trigger statements. The operators yield bridging axioms relating the different readings of the terms and, by including representations for both readings, preserve the initial ontology as well as the trigger statements. The operators differ regarding which reading of the ambiguous term is assigned to further uses of the common term and regarding the semantic relation assumed between the two readings. The ontology-revision operators are analyzed regarding their adaptability to consistent sequences of trigger statements. One group of operators (type 1) preserves all conflicts with the trigger sequence. Operators from the other group (type 2) can resolve the conflicts, which is demonstrated by showing under which conditions weak type-2 operators yield stabilizing sequences of ontologies. Stronger type-2 operators can result in closer approximations of the terminology underlying the sequence of trigger statements but can also yield non-stabilizing sequences of ontologies.

A reason maintenance perspective on relevant Ramsey conditionals

Ismail, H. O. — Wed, 12 Aug 2009 04:41:30 PDT

This paper presents a Ramsey account of conditionals within the framework of an implemented reason maintenance system. The reason maintenance system is built on top of a deductive reasoning engine based on relevance logic. Thus, the account of conditionals provided is not susceptible to the fallacies of relevance. In addition, it is shown that independently motivated requirements on practical relevant reason maintenance allow us to gracefully circumvent Gärdenfors's triviality result.

Data fusion with probabilistic conditional logic

Fisseler, J., Feher, I. — Wed, 12 Aug 2009 04:41:29 PDT

Data fusion is the process of combining data and information from two or more sources. One of its application areas is market research, where it is used to combine data sets from different surveys, yielding a joint data set. Most data fusion studies use statistical matching as their fusion algorithm, which has several drawbacks. Therefore, we propose a novel approach to data fusion, based on knowledge discovery and knowledge representation with probabilistic conditional logic. We evaluate our approach on synthetic and real-world data, demonstrating its feasibility.

Editorial: Dynamics of Knowledge and Belief

Beierle, C., Kern-Isberner, G. — Mon, 10 Aug 2009 20:55:06 PDT

An algorithm for the decomposition of finite languages

Wieczorek, W. — Sat, 08 Aug 2009 01:08:29 PDT

In this paper, an algorithm for the decomposition of a finite language is presented. The goal is to represent a finite language as a product (catenation) of two languages. This problem is thought to be intractable, although its NP-hardness has not been proven. The algorithm is based on checking through some subsets of the states of a minimal acyclic DFA. We also investigate two additional algorithms: the first is based on the use of integer linear programming, and the second is based on finding cliques in a graph. It appears that the latter approaches are inappropriate in terms of time consumption. The experiments have been performed for dozens of languages, and our results are reported.