126,079 research outputs found
Theory of higher order interpretations and application to Basic Feasible Functions
Interpretation methods and their restrictions to polynomials have been deeply
used to control the termination and complexity of first-order term rewrite
systems. This paper extends interpretation methods to a pure higher order
functional language. We develop a theory of higher order functions that is
well-suited for the complexity analysis of this programming language. The
interpretation domain is a complete lattice and, consequently, we express
program interpretation in terms of a least fixpoint. As an application, by
bounding interpretations by higher order polynomials, we characterize Basic
Feasible Functions at any order
A model of adaptive decision making from representation of information environment by quantum fields
We present the mathematical model of decision making (DM) of agents acting in
a complex and uncertain environment (combining huge variety of economical,
financial, behavioral, and geo-political factors). To describe interaction of
agents with it, we apply the formalism of quantum field theory (QTF). Quantum
fields are of the purely informational nature. The QFT-model can be treated as
a far relative of the expected utility theory, where the role of utility is
played by adaptivity to an environment (bath). However, this sort of
utility-adaptivity cannot be represented simply as a numerical function. The
operator representation in Hilbert space is used and adaptivity is described as
in quantum dynamics. We are especially interested in stabilization of solutions
for sufficiently large time. The outputs of this stabilization process,
probabilities for possible choices, are treated in the framework of classical
DM. To connect classical and quantum DM, we appeal to Quantum Bayesianism
(QBism). We demonstrate the quantum-like interference effect in DM which is
exhibited as a violation of the formula of total probability and hence the
classical Bayesian inference scheme.Comment: in press in Philosophical Transactions
The Integration of Connectionism and First-Order Knowledge Representation and Reasoning as a Challenge for Artificial Intelligence
Intelligent systems based on first-order logic on the one hand, and on
artificial neural networks (also called connectionist systems) on the other,
differ substantially. It would be very desirable to combine the robust neural
networking machinery with symbolic knowledge representation and reasoning
paradigms like logic programming in such a way that the strengths of either
paradigm will be retained. Current state-of-the-art research, however, fails by
far to achieve this ultimate goal. As one of the main obstacles to be overcome
we perceive the question how symbolic knowledge can be encoded by means of
connectionist systems: Satisfactory answers to this will naturally lead the way
to knowledge extraction algorithms and to integrated neural-symbolic systems.Comment: In Proceedings of INFORMATION'2004, Tokyo, Japan, to appear. 12 page
Constraints, Lazy Constraints, or Propagators in ASP Solving: An Empirical Analysis
Answer Set Programming (ASP) is a well-established declarative paradigm. One
of the successes of ASP is the availability of efficient systems.
State-of-the-art systems are based on the ground+solve approach. In some
applications this approach is infeasible because the grounding of one or few
constraints is expensive. In this paper, we systematically compare alternative
strategies to avoid the instantiation of problematic constraints, that are
based on custom extensions of the solver. Results on real and synthetic
benchmarks highlight some strengths and weaknesses of the different strategies.
(Under consideration for acceptance in TPLP, ICLP 2017 Special Issue.)Comment: Paper presented at the 33nd International Conference on Logic
Programming (ICLP 2017), Melbourne, Australia, August 28 to September 1,
2017. 16 page
The General Theory of Second Best Is More General Than You Think
Lipsey and Lancaster's "general theory of second best" is widely thought to have significant implications for applied theorizing about the institutions and policies that most effectively implement abstract normative principles. It is also widely thought to have little significance for theorizing about which abstract normative principles we ought to implement. Contrary to this conventional wisdom, I show how the second-best theorem can be extended to myriad domains beyond applied normative theorizing, and in particular to more abstract theorizing about the normative principles we should aim to implement. I start by separating the mathematical model used to prove the second-best theorem from its familiar economic interpretation. I then develop an alternative normative-theoretic interpretation of the model, which yields a novel second best theorem for idealistic normative theory. My method for developing this interpretation provides a template for developing additional interpretations that can extend the reach of the second-best theorem beyond normative theoretical domains. I also show how, within any domain, the implications of the second-best theorem are more specific than is typically thought. I conclude with some brief remarks on the value of mathematical models for conceptual exploration
A Topos Foundation for Theories of Physics: I. Formal Languages for Physics
This paper is the first in a series whose goal is to develop a fundamentally
new way of constructing theories of physics. The motivation comes from a desire
to address certain deep issues that arise when contemplating quantum theories
of space and time. Our basic contention is that constructing a theory of
physics is equivalent to finding a representation in a topos of a certain
formal language that is attached to the system. Classical physics arises when
the topos is the category of sets. Other types of theory employ a different
topos. In this paper we discuss two different types of language that can be
attached to a system, S. The first is a propositional language, PL(S); the
second is a higher-order, typed language L(S). Both languages provide deductive
systems with an intuitionistic logic. The reason for introducing PL(S) is that,
as shown in paper II of the series, it is the easiest way of understanding, and
expanding on, the earlier work on topos theory and quantum physics. However,
the main thrust of our programme utilises the more powerful language L(S) and
its representation in an appropriate topos.Comment: 36 pages, no figure
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