23,503 research outputs found
On a Partial Decision Method for Dynamic Proofs
This paper concerns a goal directed proof procedure for the propositional
fragment of the adaptive logic ACLuN1. At the propositional level, it forms an
algorithm for final derivability. If extended to the predicative level, it
provides a criterion for final derivability. This is essential in view of the
absence of a positive test. The procedure may be generalized to all flat
adaptive logics.Comment: 18 pages. Originally published in proc. PCL 2002, a FLoC workshop;
eds. Hendrik Decker, Dina Goldin, Jorgen Villadsen, Toshiharu Waragai
(http://floc02.diku.dk/PCL/
Convolution, Separation and Concurrency
A notion of convolution is presented in the context of formal power series
together with lifting constructions characterising algebras of such series,
which usually are quantales. A number of examples underpin the universality of
these constructions, the most prominent ones being separation logics, where
convolution is separating conjunction in an assertion quantale; interval
logics, where convolution is the chop operation; and stream interval functions,
where convolution is used for analysing the trajectories of dynamical or
real-time systems. A Hoare logic is constructed in a generic fashion on the
power series quantale, which applies to each of these examples. In many cases,
commutative notions of convolution have natural interpretations as concurrency
operations.Comment: 39 page
An approach to basic set theory and logic
The purpose of this paper is to outline a simple set of axioms for basic set
theory from which most fundamental facts can be derived. The key to the whole
project is a new axiom of set theory which I dubbed "The Law of Extremes". It
allows for quick proofs of basic set-theoretic identities and logical
tautologies, so it is also a good tool to aid one's memory.
I do not assume any exposure to euclidean geometry via axioms. Only an
experience with transforming algebraic identities is required.
The idea is to get students to do proofs right from the get-go. In
particular, I avoid entangling students in nuances of logic early on. Basic
facts of logic are derived from set theory, not the other way around.Comment: 22 page
Reasoning about Independence in Probabilistic Models of Relational Data
We extend the theory of d-separation to cases in which data instances are not
independent and identically distributed. We show that applying the rules of
d-separation directly to the structure of probabilistic models of relational
data inaccurately infers conditional independence. We introduce relational
d-separation, a theory for deriving conditional independence facts from
relational models. We provide a new representation, the abstract ground graph,
that enables a sound, complete, and computationally efficient method for
answering d-separation queries about relational models, and we present
empirical results that demonstrate effectiveness.Comment: 61 pages, substantial revisions to formalisms, theory, and related
wor
Algebraic Principles for Rely-Guarantee Style Concurrency Verification Tools
We provide simple equational principles for deriving rely-guarantee-style
inference rules and refinement laws based on idempotent semirings. We link the
algebraic layer with concrete models of programs based on languages and
execution traces. We have implemented the approach in Isabelle/HOL as a
lightweight concurrency verification tool that supports reasoning about the
control and data flow of concurrent programs with shared variables at different
levels of abstraction. This is illustrated on two simple verification examples
Program transformation for development, verification, and synthesis of programs
This paper briefly describes the use of the program transformation methodology for the development of correct and efficient programs. In particular, we will refer to the case of constraint logic programs and, through some examples, we will show how by program transformation, one can improve, synthesize, and verify programs
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