604 research outputs found
Ultimate approximations in nonmonotonic knowledge representation systems
We study fixpoints of operators on lattices. To this end we introduce the
notion of an approximation of an operator. We order approximations by means of
a precision ordering. We show that each lattice operator O has a unique most
precise or ultimate approximation. We demonstrate that fixpoints of this
ultimate approximation provide useful insights into fixpoints of the operator
O.
We apply our theory to logic programming and introduce the ultimate
Kripke-Kleene, well-founded and stable semantics. We show that the ultimate
Kripke-Kleene and well-founded semantics are more precise then their standard
counterparts We argue that ultimate semantics for logic programming have
attractive epistemological properties and that, while in general they are
computationally more complex than the standard semantics, for many classes of
theories, their complexity is no worse.Comment: This paper was published in Principles of Knowledge Representation
and Reasoning, Proceedings of the Eighth International Conference (KR2002
Epistemic Foundation of Stable Model Semantics
Stable model semantics has become a very popular approach for the management
of negation in logic programming. This approach relies mainly on the closed
world assumption to complete the available knowledge and its formulation has
its basis in the so-called Gelfond-Lifschitz transformation.
The primary goal of this work is to present an alternative and
epistemic-based characterization of stable model semantics, to the
Gelfond-Lifschitz transformation. In particular, we show that stable model
semantics can be defined entirely as an extension of the Kripke-Kleene
semantics. Indeed, we show that the closed world assumption can be seen as an
additional source of `falsehood' to be added cumulatively to the Kripke-Kleene
semantics. Our approach is purely algebraic and can abstract from the
particular formalism of choice as it is based on monotone operators (under the
knowledge order) over bilattices only.Comment: 41 pages. To appear in Theory and Practice of Logic Programming
(TPLP
A Canonical Model Construction for Iteration-Free PDL with Intersection
We study the axiomatisability of the iteration-free fragment of Propositional
Dynamic Logic with Intersection and Tests. The combination of program
composition, intersection and tests makes its proof-theory rather difficult. We
develop a normal form for formulae which minimises the interaction between
these operators, as well as a refined canonical model construction. From these
we derive an axiom system and a proof of its strong completeness.Comment: In Proceedings GandALF 2016, arXiv:1609.0364
Applying Formal Methods to Networking: Theory, Techniques and Applications
Despite its great importance, modern network infrastructure is remarkable for
the lack of rigor in its engineering. The Internet which began as a research
experiment was never designed to handle the users and applications it hosts
today. The lack of formalization of the Internet architecture meant limited
abstractions and modularity, especially for the control and management planes,
thus requiring for every new need a new protocol built from scratch. This led
to an unwieldy ossified Internet architecture resistant to any attempts at
formal verification, and an Internet culture where expediency and pragmatism
are favored over formal correctness. Fortunately, recent work in the space of
clean slate Internet design---especially, the software defined networking (SDN)
paradigm---offers the Internet community another chance to develop the right
kind of architecture and abstractions. This has also led to a great resurgence
in interest of applying formal methods to specification, verification, and
synthesis of networking protocols and applications. In this paper, we present a
self-contained tutorial of the formidable amount of work that has been done in
formal methods, and present a survey of its applications to networking.Comment: 30 pages, submitted to IEEE Communications Surveys and Tutorial
Kleene algebra with domain
We propose Kleene algebra with domain (KAD), an extension of Kleene algebra
with two equational axioms for a domain and a codomain operation, respectively.
KAD considerably augments the expressiveness of Kleene algebra, in particular
for the specification and analysis of state transition systems. We develop the
basic calculus, discuss some related theories and present the most important
models of KAD. We demonstrate applicability by two examples: First, an
algebraic reconstruction of Noethericity and well-foundedness; second, an
algebraic reconstruction of propositional Hoare logic.Comment: 40 page
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