Computable Aggregations

In this paper, we postulate computation as a key element in assuring the consistency of a family of aggregation functions so that such a family of operators can be considered an aggregation rule. In particular, we suggest that the concept of an aggregation rule should be defined from a computational point of view, focusing on the computational properties of such an aggregation, i.e., on the manner in which the aggregation values are computed. The new algorithmic definition of aggregation we propose provides an operational approach to aggregation, one that is based upon lists of variable length and that produces a solution even when portions of data are inserted or deleted. Among other advantages, this approach allows the construction of different classifications of aggregation rules according to the programming paradigms used for their computation or according to their computational complexity

Complexity, parallel computation and statistical physics

The intuition that a long history is required for the emergence of complexity in natural systems is formalized using the notion of depth. The depth of a system is defined in terms of the number of parallel computational steps needed to simulate it. Depth provides an objective, irreducible measure of history applicable to systems of the kind studied in statistical physics. It is argued that physical complexity cannot occur in the absence of substantial depth and that depth is a useful proxy for physical complexity. The ideas are illustrated for a variety of systems in statistical physics.Comment: 21 pages, 7 figure

On the cost-complexity of multi-context systems

Multi-context systems provide a powerful framework for modelling information-aggregation systems featuring heterogeneous reasoning components. Their execution can, however, incur non-negligible cost. Here, we focus on cost-complexity of such systems. To that end, we introduce cost-aware multi-context systems, an extension of non-monotonic multi-context systems framework taking into account costs incurred by execution of semantic operators of the individual contexts. We formulate the notion of cost-complexity for consistency and reasoning problems in MCSs. Subsequently, we provide a series of results related to gradually more and more constrained classes of MCSs and finally introduce an incremental cost-reducing algorithm solving the reasoning problem for definite MCSs

A Framework for Approval-based Budgeting Methods

We define and study a general framework for approval-based budgeting methods and compare certain methods within this framework by their axiomatic and computational properties. Furthermore, we visualize their behavior on certain Euclidean distributions and analyze them experimentally

Preservation of Semantic Properties during the Aggregation of Abstract Argumentation Frameworks

An abstract argumentation framework can be used to model the argumentative stance of an agent at a high level of abstraction, by indicating for every pair of arguments that is being considered in a debate whether the first attacks the second. When modelling a group of agents engaged in a debate, we may wish to aggregate their individual argumentation frameworks to obtain a single such framework that reflects the consensus of the group. Even when agents disagree on many details, there may well be high-level agreement on important semantic properties, such as the acceptability of a given argument. Using techniques from social choice theory, we analyse under what circumstances such semantic properties agreed upon by the individual agents can be preserved under aggregation.Comment: In Proceedings TARK 2017, arXiv:1707.0825

Language acquisition and machine learning

In this paper, we review recent progress in the field of machine learning and examine its implications for computational models of language acquisition. As a framework for understanding this research, we propose four component tasks involved in learning from experience - aggregation, clustering, characterization, and storage. We then consider four common problems studied by machine learning researchers - learning from examples, heuristics learning, conceptual clustering, and learning macro-operators - describing each in terms of our framework. After this, we turn to the problem of grammar acquisition, relating this problem to other learning tasks and reviewing four AI systems that have addressed the problem. Finally, we note some limitations of the earlier work and propose an alternative approach to modeling the mechanisms underlying language acquisition