26,413 research outputs found
Subset models for justification logic
We introduce a new semantics for justification logic based on subset
relations. Instead of using the established and more symbolic interpretation of
justifications, we model justifications as sets of possible worlds. We
introduce a new justification logic that is sound and complete with respect to
our semantics. Moreover, we present another variant of our semantics that
corresponds to traditional justification logic.
These types of models offer us a versatile tool to work with justifications,
e.g.~by extending them with a probability measure to capture uncertain
justifications. Following this strategy we will show that they subsume
Artemov's approach to aggregating probabilistic evidence
Probability Logic for Harsanyi Type Spaces
Probability logic has contributed to significant developments in belief types
for game-theoretical economics. We present a new probability logic for Harsanyi
Type spaces, show its completeness, and prove both a de-nesting property and a
unique extension theorem. We then prove that multi-agent interactive
epistemology has greater complexity than its single-agent counterpart by
showing that if the probability indices of the belief language are restricted
to a finite set of rationals and there are finitely many propositional letters,
then the canonical space for probabilistic beliefs with one agent is finite
while the canonical one with at least two agents has the cardinality of the
continuum. Finally, we generalize the three notions of definability in
multimodal logics to logics of probabilistic belief and knowledge, namely
implicit definability, reducibility, and explicit definability. We find that
S5-knowledge can be implicitly defined by probabilistic belief but not reduced
to it and hence is not explicitly definable by probabilistic belief
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Logics of Imprecise Comparative Probability
This paper studies connections between two alternatives to the standard probability calculus for representing and reasoning about uncertainty: imprecise probability andcomparative probability. The goal is to identify complete logics for reasoning about uncertainty in a comparative probabilistic language whose semantics is given in terms of imprecise probability. Comparative probability operators are interpreted as quantifying over a set of probability measures. Modal and dynamic operators are added for reasoning about epistemic possibility and updating sets of probability measures
On theories of random variables
We study theories of spaces of random variables: first, we consider random
variables with values in the interval , then with values in an arbitrary
metric structure, generalising Keisler's randomisation of classical structures.
We prove preservation and non-preservation results for model theoretic
properties under this construction: i) The randomisation of a stable structure
is stable. ii) The randomisation of a simple unstable structure is not simple.
We also prove that in the randomised structure, every type is a Lascar type
Incremental Control Synthesis in Probabilistic Environments with Temporal Logic Constraints
In this paper, we present a method for optimal control synthesis of a plant
that interacts with a set of agents in a graph-like environment. The control
specification is given as a temporal logic statement about some properties that
hold at the vertices of the environment. The plant is assumed to be
deterministic, while the agents are probabilistic Markov models. The goal is to
control the plant such that the probability of satisfying a syntactically
co-safe Linear Temporal Logic formula is maximized. We propose a
computationally efficient incremental approach based on the fact that temporal
logic verification is computationally cheaper than synthesis. We present a
case-study where we compare our approach to the classical non-incremental
approach in terms of computation time and memory usage.Comment: Extended version of the CDC 2012 pape
A temporal semantics for Nilpotent Minimum logic
In [Ban97] a connection among rough sets (in particular, pre-rough algebras)
and three-valued {\L}ukasiewicz logic {\L}3 is pointed out. In this paper we
present a temporal like semantics for Nilpotent Minimum logic NM ([Fod95,
EG01]), in which the logic of every instant is given by {\L}3: a completeness
theorem will be shown. This is the prosecution of the work initiated in [AGM08]
and [ABM09], in which the authors construct a temporal semantics for the
many-valued logics of G\"odel ([G\"od32], [Dum59]) and Basic Logic ([H\'aj98]).Comment: 19 pages, 2 table
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