232 research outputs found
Probability Aggregates in Probability Answer Set Programming
Probability answer set programming is a declarative programming that has been
shown effective for representing and reasoning about a variety of probability
reasoning tasks. However, the lack of probability aggregates, e.g. {\em
expected values}, in the language of disjunctive hybrid probability logic
programs (DHPP) disallows the natural and concise representation of many
interesting problems. In this paper, we extend DHPP to allow arbitrary
probability aggregates. We introduce two types of probability aggregates; a
type that computes the expected value of a classical aggregate, e.g., the
expected value of the minimum, and a type that computes the probability of a
classical aggregate, e.g, the probability of sum of values. In addition, we
define a probability answer set semantics for DHPP with arbitrary probability
aggregates including monotone, antimonotone, and nonmonotone probability
aggregates. We show that the proposed probability answer set semantics of DHPP
subsumes both the original probability answer set semantics of DHPP and the
classical answer set semantics of classical disjunctive logic programs with
classical aggregates, and consequently subsumes the classical answer set
semantics of the original disjunctive logic programs. We show that the proposed
probability answer sets of DHPP with probability aggregates are minimal
probability models and hence incomparable, which is an important property for
nonmonotonic probability reasoning
Logical Fuzzy Optimization
We present a logical framework to represent and reason about fuzzy
optimization problems based on fuzzy answer set optimization programming. This
is accomplished by allowing fuzzy optimization aggregates, e.g., minimum and
maximum in the language of fuzzy answer set optimization programming to allow
minimization or maximization of some desired criteria under fuzzy environments.
We show the application of the proposed logical fuzzy optimization framework
under the fuzzy answer set optimization programming to the fuzzy water
allocation optimization problem
Logical Stochastic Optimization
We present a logical framework to represent and reason about stochastic
optimization problems based on probability answer set programming. This is
established by allowing probability optimization aggregates, e.g., minimum and
maximum in the language of probability answer set programming to allow
minimization or maximization of some desired criteria under the probabilistic
environments. We show the application of the proposed logical stochastic
optimization framework under the probability answer set programming to two
stages stochastic optimization problems with recourse.Comment: arXiv admin note: substantial text overlap with arXiv:1304.2384,
arXiv:1304.2797, arXiv:1304.1684, arXiv:1304.314
Logical Fuzzy Preferences
We present a unified logical framework for representing and reasoning about
both quantitative and qualitative preferences in fuzzy answer set programming,
called fuzzy answer set optimization programs. The proposed framework is vital
to allow defining quantitative preferences over the possible outcomes of
qualitative preferences. We show the application of fuzzy answer set
optimization programs to the course scheduling with fuzzy preferences problem.
To the best of our knowledge, this development is the first to consider a
logical framework for reasoning about quantitative preferences, in general, and
reasoning about both quantitative and qualitative preferences in particular.Comment: arXiv admin note: substantial text overlap with arXiv:1304.238
Logical Probability Preferences
We present a unified logical framework for representing and reasoning about
both probability quantitative and qualitative preferences in probability answer
set programming, called probability answer set optimization programs. The
proposed framework is vital to allow defining probability quantitative
preferences over the possible outcomes of qualitative preferences. We show the
application of probability answer set optimization programs to a variant of the
well-known nurse restoring problem, called the nurse restoring with probability
preferences problem. To the best of our knowledge, this development is the
first to consider a logical framework for reasoning about probability
quantitative preferences, in general, and reasoning about both probability
quantitative and qualitative preferences in particular.Comment: arXiv admin note: substantial text overlap with arXiv:1304.2384,
arXiv:1304.279
Non Deterministic Logic Programs
Non deterministic applications arise in many domains, including, stochastic
optimization, multi-objectives optimization, stochastic planning, contingent
stochastic planning, reinforcement learning, reinforcement learning in
partially observable Markov decision processes, and conditional planning. We
present a logic programming framework called non deterministic logic programs,
along with a declarative semantics and fixpoint semantics, to allow
representing and reasoning about inherently non deterministic real-world
applications. The language of non deterministic logic programs framework is
extended with non-monotonic negation, and two alternative semantics are
defined: the stable non deterministic model semantics and the well-founded non
deterministic model semantics as well as their relationship is studied. These
semantics subsume the deterministic stable model semantics and the
deterministic well-founded semantics of deterministic normal logic programs,
and they reduce to the semantics of deterministic definite logic programs
without negation. We show the application of the non deterministic logic
programs framework to a conditional planning problem
Nested Aggregates in Answer Sets: An Application to a Priori Optimization
We allow representing and reasoning in the presence of nested multiple
aggregates over multiple variables and nested multiple aggregates over
functions involving multiple variables in answer sets, precisely, in answer set
optimization programming and in answer set programming. We show the
applicability of the answer set optimization programming with nested multiple
aggregates and the answer set programming with nested multiple aggregates to
the Probabilistic Traveling Salesman Problem, a fundamental a priori
optimization problem in Operation Research.Comment: arXiv admin note: text overlap with arXiv:1304.238
Reinforcement Learning in Partially Observable Markov Decision Processes using Hybrid Probabilistic Logic Programs
We present a probabilistic logic programming framework to reinforcement
learning, by integrating reinforce-ment learning, in POMDP environments, with
normal hybrid probabilistic logic programs with probabilistic answer set
seman-tics, that is capable of representing domain-specific knowledge. We
formally prove the correctness of our approach. We show that the complexity of
finding a policy for a reinforcement learning problem in our approach is
NP-complete. In addition, we show that any reinforcement learning problem can
be encoded as a classical logic program with answer set semantics. We also show
that a reinforcement learning problem can be encoded as a SAT problem. We
present a new high level action description language that allows the factored
representation of POMDP. Moreover, we modify the original model of POMDP so
that it be able to distinguish between knowledge producing actions and actions
that change the environment
Bridging the Gap between Reinforcement Learning and Knowledge Representation: A Logical Off- and On-Policy Framework
Knowledge Representation is important issue in reinforcement learning. In
this paper, we bridge the gap between reinforcement learning and knowledge
representation, by providing a rich knowledge representation framework, based
on normal logic programs with answer set semantics, that is capable of solving
model-free reinforcement learning problems for more complex do-mains and
exploits the domain-specific knowledge. We prove the correctness of our
approach. We show that the complexity of finding an offline and online policy
for a model-free reinforcement learning problem in our approach is NP-complete.
Moreover, we show that any model-free reinforcement learning problem in MDP
environment can be encoded as a SAT problem. The importance of that is
model-free reinforcemen
Fuzzy Aggregates in Fuzzy Answer Set Programming
Fuzzy answer set programming is a declarative framework for representing and
reasoning about knowledge in fuzzy environments. However, the unavailability of
fuzzy aggregates in disjunctive fuzzy logic programs, DFLP, with fuzzy answer
set semantics prohibits the natural and concise representation of many
interesting problems. In this paper, we extend DFLP to allow arbitrary fuzzy
aggregates. We define fuzzy answer set semantics for DFLP with arbitrary fuzzy
aggregates including monotone, antimonotone, and nonmonotone fuzzy aggregates.
We show that the proposed fuzzy answer set semantics subsumes both the original
fuzzy answer set semantics of DFLP and the classical answer set semantics of
classical disjunctive logic programs with classical aggregates, and
consequently subsumes the classical answer set semantics of classical
disjunctive logic programs. We show that the proposed fuzzy answer sets of DFLP
with fuzzy aggregates are minimal fuzzy models and hence incomparable, which is
an important property for nonmonotonic fuzzy reasoning.Comment: arXiv admin note: substantial text overlap with arXiv:1304.168
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