202,020 research outputs found
A hybrid model for sharing information between fuzzy, uncertain and default reasoning models in multi-agent systems
This paper develops a hybrid model which provides a unified framework for the following four kinds of reasoning: 1)Zadeh's fuzzy approximate reasoning; 2) Truth qualification uncertain reasoning with respect to fuzzy propositions; 3)fuzzy default reasoning (proposed, in this paper, as an extension of Reiter's default reasoning); and 4)truth- qualification uncertain default reasoning associated with fuzzy statements (developed in this paper to enrich fuzzy default reasoning with uncertain information). Our hybrid model has the following characteristics: 1) basic uncertainty is estimated in terms of words or phrases in natural language and basic propositions are fuzzy; 2) uncertainty, linguistically expressed, can be handled in default reasoning; and 3) the four kinds of reasoning models mentioned above and their combination models will be the special cases of our hybrid model. Moreover, our model allows the reasoning to be performed in the case in which the information is fuzzy, uncertain and partial. More importantly, the problems of sharing the information among heterogenous fuzzy, uncertain and default reasoning models can be solved efficiently by using our model. Given this, our framework can be used as a basis for information sharing and exchange in knowledge-based multi-agent systems for practical applications such as automated group negotiations. Actually, to build such a foundation is the motivation of this paper
Named Models in Coalgebraic Hybrid Logic
Hybrid logic extends modal logic with support for reasoning about individual
states, designated by so-called nominals. We study hybrid logic in the broad
context of coalgebraic semantics, where Kripke frames are replaced with
coalgebras for a given functor, thus covering a wide range of reasoning
principles including, e.g., probabilistic, graded, default, or coalitional
operators. Specifically, we establish generic criteria for a given coalgebraic
hybrid logic to admit named canonical models, with ensuing completeness proofs
for pure extensions on the one hand, and for an extended hybrid language with
local binding on the other. We instantiate our framework with a number of
examples. Notably, we prove completeness of graded hybrid logic with local
binding
KR: An Architecture for Knowledge Representation and Reasoning in Robotics
This paper describes an architecture that combines the complementary
strengths of declarative programming and probabilistic graphical models to
enable robots to represent, reason with, and learn from, qualitative and
quantitative descriptions of uncertainty and knowledge. An action language is
used for the low-level (LL) and high-level (HL) system descriptions in the
architecture, and the definition of recorded histories in the HL is expanded to
allow prioritized defaults. For any given goal, tentative plans created in the
HL using default knowledge and commonsense reasoning are implemented in the LL
using probabilistic algorithms, with the corresponding observations used to
update the HL history. Tight coupling between the two levels enables automatic
selection of relevant variables and generation of suitable action policies in
the LL for each HL action, and supports reasoning with violation of defaults,
noisy observations and unreliable actions in large and complex domains. The
architecture is evaluated in simulation and on physical robots transporting
objects in indoor domains; the benefit on robots is a reduction in task
execution time of 39% compared with a purely probabilistic, but still
hierarchical, approach.Comment: The paper appears in the Proceedings of the 15th International
Workshop on Non-Monotonic Reasoning (NMR 2014
Complexity of Non-Monotonic Logics
Over the past few decades, non-monotonic reasoning has developed to be one of
the most important topics in computational logic and artificial intelligence.
Different ways to introduce non-monotonic aspects to classical logic have been
considered, e.g., extension with default rules, extension with modal belief
operators, or modification of the semantics. In this survey we consider a
logical formalism from each of the above possibilities, namely Reiter's default
logic, Moore's autoepistemic logic and McCarthy's circumscription.
Additionally, we consider abduction, where one is not interested in inferences
from a given knowledge base but in computing possible explanations for an
observation with respect to a given knowledge base.
Complexity results for different reasoning tasks for propositional variants
of these logics have been studied already in the nineties. In recent years,
however, a renewed interest in complexity issues can be observed. One current
focal approach is to consider parameterized problems and identify reasonable
parameters that allow for FPT algorithms. In another approach, the emphasis
lies on identifying fragments, i.e., restriction of the logical language, that
allow more efficient algorithms for the most important reasoning tasks. In this
survey we focus on this second aspect. We describe complexity results for
fragments of logical languages obtained by either restricting the allowed set
of operators (e.g., forbidding negations one might consider only monotone
formulae) or by considering only formulae in conjunctive normal form but with
generalized clause types.
The algorithmic problems we consider are suitable variants of satisfiability
and implication in each of the logics, but also counting problems, where one is
not only interested in the existence of certain objects (e.g., models of a
formula) but asks for their number.Comment: To appear in Bulletin of the EATC
Space Efficiency of Propositional Knowledge Representation Formalisms
We investigate the space efficiency of a Propositional Knowledge
Representation (PKR) formalism. Intuitively, the space efficiency of a
formalism F in representing a certain piece of knowledge A, is the size of the
shortest formula of F that represents A. In this paper we assume that knowledge
is either a set of propositional interpretations (models) or a set of
propositional formulae (theorems). We provide a formal way of talking about the
relative ability of PKR formalisms to compactly represent a set of models or a
set of theorems. We introduce two new compactness measures, the corresponding
classes, and show that the relative space efficiency of a PKR formalism in
representing models/theorems is directly related to such classes. In
particular, we consider formalisms for nonmonotonic reasoning, such as
circumscription and default logic, as well as belief revision operators and the
stable model semantics for logic programs with negation. One interesting result
is that formalisms with the same time complexity do not necessarily belong to
the same space efficiency class
Graph theoretical structures in logic programs and default theories
In this paper we present a graph representation of logic programs and default theories. We show that many of the semantics proposed for logic programs can be expressed in terms of notions emerging from graph theory, establishing in this way a link between the fields. Namely the stable models, the partial stable models, and the well-founded semantics correspond respectively to the kernels, semikernels and the initial acyclic part of the associated graph. This link allows us to consider both theoretical problems (existence, uniqueness) and computational problems (tractability, algorithms, approximations) from a more abstract and rather combinatorial point of view. It also provides a clear and intuitive understanding about how conflicts between rules are resolved within the different semantics. Furthermore, we extend the basic framework developed for logic programs to the case of Default Logic by introducing the notions of partial, deterministic and well-founded extensions for default theories. These semantics capture different ways of reasoning with a default theory
Named Models in Coalgebraic Hybrid Logic
Hybrid logic extends modal logic with support for reasoning about individual states, designated by so-called nominals. We study hybrid
logic in the broad context of coalgebraic semantics, where Kripke frames are replaced with coalgebras for a given functor, thus covering a wide range of reasoning principles including, e.g., probabilistic, graded, default, or coalitional operators. Specifically, we establish generic criteria for a given coalgebraic hybrid logic to admit named canonical models, with ensuing completeness proofs for pure extensions on the one hand, and for an extended hybrid language with local binding on the other. We instantiate our framework with a number of examples. Notably, we prove completeness of graded hybrid logic with local binding
Flexible Invariants Through Semantic Collaboration
Modular reasoning about class invariants is challenging in the presence of
dependencies among collaborating objects that need to maintain global
consistency. This paper presents semantic collaboration: a novel methodology to
specify and reason about class invariants of sequential object-oriented
programs, which models dependencies between collaborating objects by semantic
means. Combined with a simple ownership mechanism and useful default schemes,
semantic collaboration achieves the flexibility necessary to reason about
complicated inter-object dependencies but requires limited annotation burden
when applied to standard specification patterns. The methodology is implemented
in AutoProof, our program verifier for the Eiffel programming language (but it
is applicable to any language supporting some form of representation
invariants). An evaluation on several challenge problems proposed in the
literature demonstrates that it can handle a variety of idiomatic collaboration
patterns, and is more widely applicable than the existing invariant
methodologies.Comment: 22 page
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