31,695 research outputs found
Metric Semantics and Full Abstractness for Action Refinement and Probabilistic Choice
This paper provides a case-study in the field of metric semantics for probabilistic programming. Both an operational and a denotational semantics are presented for an abstract process language L_pr, which features action refinement and probabilistic choice. The two models are constructed in the setting of complete ultrametric spaces, here based on probability measures of compact support over sequences of actions. It is shown that the standard toolkit for metric semantics works well in the probabilistic context of L_pr, e.g. in establishing the correctness of the denotational semantics with respect to the operational one. In addition, it is shown how the method of proving full abstraction --as proposed recently by the authors for a nondeterministic language with action refinement-- can be adapted to deal with the probabilistic language L_pr as well
Probabilistic Interval Temporal Logic and Duration Calculus with Infinite Intervals: Complete Proof Systems
The paper presents probabilistic extensions of interval temporal logic (ITL)
and duration calculus (DC) with infinite intervals and complete Hilbert-style
proof systems for them. The completeness results are a strong completeness
theorem for the system of probabilistic ITL with respect to an abstract
semantics and a relative completeness theorem for the system of probabilistic
DC with respect to real-time semantics. The proposed systems subsume
probabilistic real-time DC as known from the literature. A correspondence
between the proposed systems and a system of probabilistic interval temporal
logic with finite intervals and expanding modalities is established too.Comment: 43 page
Probabilistic Operational Semantics for the Lambda Calculus
Probabilistic operational semantics for a nondeterministic extension of pure
lambda calculus is studied. In this semantics, a term evaluates to a (finite or
infinite) distribution of values. Small-step and big-step semantics are both
inductively and coinductively defined. Moreover, small-step and big-step
semantics are shown to produce identical outcomes, both in call-by- value and
in call-by-name. Plotkin's CPS translation is extended to accommodate the
choice operator and shown correct with respect to the operational semantics.
Finally, the expressive power of the obtained system is studied: the calculus
is shown to be sound and complete with respect to computable probability
distributions.Comment: 35 page
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