A decidable subclass of finitary programs

Answer set programming - the most popular problem solving paradigm based on logic programs - has been recently extended to support uninterpreted function symbols. All of these approaches have some limitation. In this paper we propose a class of programs called FP2 that enjoys a different trade-off between expressiveness and complexity. FP2 programs enjoy the following unique combination of properties: (i) the ability of expressing predicates with infinite extensions; (ii) full support for predicates with arbitrary arity; (iii) decidability of FP2 membership checking; (iv) decidability of skeptical and credulous stable model reasoning for call-safe queries. Odd cycles are supported by composing FP2 programs with argument restricted programs

On finitely recursive programs

Disjunctive finitary programs are a class of logic programs admitting function symbols and hence infinite domains. They have very good computational properties, for example ground queries are decidable while in the general case the stable model semantics is highly undecidable. In this paper we prove that a larger class of programs, called finitely recursive programs, preserves most of the good properties of finitary programs under the stable model semantics, namely: (i) finitely recursive programs enjoy a compactness property; (ii) inconsistency checking and skeptical reasoning are semidecidable; (iii) skeptical resolution is complete for normal finitely recursive programs. Moreover, we show how to check inconsistency and answer skeptical queries using finite subsets of the ground program instantiation. We achieve this by extending the splitting sequence theorem by Lifschitz and Turner: We prove that if the input program P is finitely recursive, then the partial stable models determined by any smooth splitting omega-sequence converge to a stable model of P.Comment: 26 pages, Preliminary version in Proc. of ICLP 2007, Best paper awar

Platonic model of mind as an approximation to neurodynamics

Hierarchy of approximations involved in simplification of microscopic theories, from sub-cellural to the whole brain level, is presented. A new approximation to neural dynamics is described, leading to a Platonic-like model of mind based on psychological spaces. Objects and events in these spaces correspond to quasi-stable states of brain dynamics and may be interpreted from psychological point of view. Platonic model bridges the gap between neurosciences and psychological sciences. Static and dynamic versions of this model are outlined and Feature Space Mapping, a neurofuzzy realization of the static version of Platonic model, described. Categorization experiments with human subjects are analyzed from the neurodynamical and Platonic model points of view

Computational physics of the mind

In the XIX century and earlier such physicists as Newton, Mayer, Hooke, Helmholtz and Mach were actively engaged in the research on psychophysics, trying to relate psychological sensations to intensities of physical stimuli. Computational physics allows to simulate complex neural processes giving a chance to answer not only the original psychophysical questions but also to create models of mind. In this paper several approaches relevant to modeling of mind are outlined. Since direct modeling of the brain functions is rather limited due to the complexity of such models a number of approximations is introduced. The path from the brain, or computational neurosciences, to the mind, or cognitive sciences, is sketched, with emphasis on higher cognitive functions such as memory and consciousness. No fundamental problems in understanding of the mind seem to arise. From computational point of view realistic models require massively parallel architectures

Computing Preferred Answer Sets by Meta-Interpretation in Answer Set Programming

Most recently, Answer Set Programming (ASP) is attracting interest as a new paradigm for problem solving. An important aspect which needs to be supported is the handling of preferences between rules, for which several approaches have been presented. In this paper, we consider the problem of implementing preference handling approaches by means of meta-interpreters in Answer Set Programming. In particular, we consider the preferred answer set approaches by Brewka and Eiter, by Delgrande, Schaub and Tompits, and by Wang, Zhou and Lin. We present suitable meta-interpreters for these semantics using DLV, which is an efficient engine for ASP. Moreover, we also present a meta-interpreter for the weakly preferred answer set approach by Brewka and Eiter, which uses the weak constraint feature of DLV as a tool for expressing and solving an underlying optimization problem. We also consider advanced meta-interpreters, which make use of graph-based characterizations and often allow for more efficient computations. Our approach shows the suitability of ASP in general and of DLV in particular for fast prototyping. This can be fruitfully exploited for experimenting with new languages and knowledge-representation formalisms.Comment: 34 pages, appeared as a Technical Report at KBS of the Vienna University of Technology, see http://www.kr.tuwien.ac.at/research/reports

A Review of Findings from Neuroscience and Cognitive Psychology as Possible Inspiration for the Path to Artificial General Intelligence

This review aims to contribute to the quest for artificial general intelligence by examining neuroscience and cognitive psychology methods for potential inspiration. Despite the impressive advancements achieved by deep learning models in various domains, they still have shortcomings in abstract reasoning and causal understanding. Such capabilities should be ultimately integrated into artificial intelligence systems in order to surpass data-driven limitations and support decision making in a way more similar to human intelligence. This work is a vertical review that attempts a wide-ranging exploration of brain function, spanning from lower-level biological neurons, spiking neural networks, and neuronal ensembles to higher-level concepts such as brain anatomy, vector symbolic architectures, cognitive and categorization models, and cognitive architectures. The hope is that these concepts may offer insights for solutions in artificial general intelligence.Comment: 143 pages, 49 figures, 244 reference

Order in glassy systems

A directly measurable correlation length may be defined for systems having a two-step relaxation, based on the geometric properties of density profile that remains after averaging out the fast motion. We argue that the length diverges if and when the slow timescale diverges, whatever the microscopic mechanism at the origin of the slowing down. Measuring the length amounts to determining explicitly the complexity from the observed particle configurations. One may compute in the same way the Renyi complexities K_q, their relative behavior for different q characterizes the mechanism underlying the transition. In particular, the 'Random First Order' scenario predicts that in the glass phase K_q=0 for q>x, and K_q>0 for q<x, with x the Parisi parameter. The hypothesis of a nonequilibrium effective temperature may also be directly tested directly from configurations.Comment: Typos corrected, clarifications adde