272,527 research outputs found
Bounded Arithmetic in Free Logic
One of the central open questions in bounded arithmetic is whether Buss'
hierarchy of theories of bounded arithmetic collapses or not. In this paper, we
reformulate Buss' theories using free logic and conjecture that such theories
are easier to handle. To show this, we first prove that Buss' theories prove
consistencies of induction-free fragments of our theories whose formulae have
bounded complexity. Next, we prove that although our theories are based on an
apparently weaker logic, we can interpret theories in Buss' hierarchy by our
theories using a simple translation. Finally, we investigate finitistic G\"odel
sentences in our systems in the hope of proving that a theory in a lower level
of Buss' hierarchy cannot prove consistency of induction-free fragments of our
theories whose formulae have higher complexity
Progression and Verification of Situation Calculus Agents with Bounded Beliefs
We investigate agents that have incomplete information and make decisions based on their beliefs expressed as situation calculus bounded action theories. Such theories have an infinite object domain, but the number of objects that belong to fluents at each time point is bounded by a given constant. Recently, it has been shown that verifying temporal properties over such theories is decidable. We take a first-person view and use the theory to capture what the agent believes about the domain of interest and the actions affecting it. In this paper, we study verification of temporal properties over online executions. These are executions resulting from agents performing only actions that are feasible according to their beliefs. To do so, we first examine progression, which captures belief state update resulting from actions in the situation calculus. We show that, for bounded action theories, progression, and hence belief states, can always be represented as a bounded first-order logic theory. Then, based on this result, we prove decidability of temporal verification over online executions for bounded action theories. © 2015 The Author(s
The dynamics of wind-driven intraseasonal variability in the equatorial Indian Ocean
This commentary provides a discussion of the concept of `bounded rationality' as it applies to the theses advanced by Lopes (1991) and Evans (1991). Lopes's (1991) assessment of the irrationalist consequences of Tversky and Kahneman's (1974) work on heuristics and biases is premature because bounded rationality implies that people could not employ optimal strategies. Considerations of bounded rationality also provide additional criteria by which to judge the theories of deductive reasoning discussed by Evans (1991). Judged by this criterion, theories whose goal is to explain logically competent performance are inadequate (Oaksford & Chater, 1991). Thus Evans's assessment of the state of current theories of reasoning requires revision
On Rules and Parameter Free Systems in Bounded Arithmetic
We present model–theoretic techniques to obtain conservation
results for first order bounded arithmetic theories, based on a hierarchical
version of the well known notion of an existentially closed model.Ministerio de Educación y Ciencia MTM2005-0865
On First-Order μ-Calculus over Situation Calculus Action Theories
In this paper we study verification of situation calculus action theories against first-order mu-calculus with quantification across situations. Specifically, we consider mu-La and mu-Lp, the two variants of mu-calculus introduced in the literature for verification of data-aware processes. The former requires that quantification ranges over objects in the current active domain, while the latter additionally requires that objects assigned to variables persist across situations. Each of these two logics has a distinct corresponding notion of bisimulation. In spite of the differences we show that the two notions of bisimulation collapse for dynamic systems that are generic, which include all those systems specified through a situation calculus action theory. Then, by exploiting this result, we show that for bounded situation calculus action theories, mu-La and mu-Lp have exactly the same expressive power. Finally, we prove decidability of verification of mu-La properties over bounded action theories, using finite faithful abstractions. Differently from the mu-Lp case, these abstractions must depend on the number of quantified variables in the mu-La formula
Universal thermodynamics in different gravity theories: Modified entropy on the horizons
The paper deals with universal thermodynamics for FRW model of the universe
bounded by apparent (or event) horizon. Assuming Hawking temperature on the
horizon, the unified first law is examined on the horizon for different gravity
theories. The results show that equilibrium configuration is preserved with a
modification to Bekenstein entropy on the horizon
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