12,996 research outputs found
Finding Minimal Cost Herbrand Models with Branch-Cut-and-Price
Given (1) a set of clauses in some first-order language and (2)
a cost function , mapping each
ground atom in the Herbrand base to a non-negative real, then
the problem of finding a minimal cost Herbrand model is to either find a
Herbrand model of which is guaranteed to minimise the sum of the
costs of true ground atoms, or establish that there is no Herbrand model for
. A branch-cut-and-price integer programming (IP) approach to solving this
problem is presented. Since the number of ground instantiations of clauses and
the size of the Herbrand base are both infinite in general, we add the
corresponding IP constraints and IP variables `on the fly' via `cutting' and
`pricing' respectively. In the special case of a finite Herbrand base we show
that adding all IP variables and constraints from the outset can be
advantageous, showing that a challenging Markov logic network MAP problem can
be solved in this way if encoded appropriately
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Transformation of propositional calculus statements into integer and mixed integer programs: An approach towards automatic reformulation
A systematic procedure for transforming a set of logical statements or logical conditions imposed on a model into an Integer Linear Progamming (ILP) formulation Mixed Integer Programming (MIP) formulation is presented. An ILP stated as a system of linear constraints involving integer variables and an objective function, provides a powerful representation of decision problems through a tightly interrelated closed system of choices. It supports direct representation of logical (Boolean or prepositional calculus) expressions. Binary variables (hereafter called logical variables) are first introduced and methods of logically connecting these to other variables are then presented. Simple constraints can be combined to construct logical relationships and the methods of formulating these are discussed. A reformulation procedure which uses the extended reverse polish representation of a compound logical form is then described. These reformulation procedures are illustrated by two examples. A scheme of implementation.ithin an LP modelling system is outlined
TreatJS: Higher-Order Contracts for JavaScript
TreatJS is a language embedded, higher-order contract system for JavaScript
which enforces contracts by run-time monitoring. Beyond providing the standard
abstractions for building higher-order contracts (base, function, and object
contracts), TreatJS's novel contributions are its guarantee of non-interfering
contract execution, its systematic approach to blame assignment, its support
for contracts in the style of union and intersection types, and its notion of a
parameterized contract scope, which is the building block for composable
run-time generated contracts that generalize dependent function contracts.
TreatJS is implemented as a library so that all aspects of a contract can be
specified using the full JavaScript language. The library relies on JavaScript
proxies to guarantee full interposition for contracts. It further exploits
JavaScript's reflective features to run contracts in a sandbox environment,
which guarantees that the execution of contract code does not modify the
application state. No source code transformation or change in the JavaScript
run-time system is required.
The impact of contracts on execution speed is evaluated using the Google
Octane benchmark.Comment: Technical Repor
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
From IF to BI: a tale of dependence and separation
We take a fresh look at the logics of informational dependence and
independence of Hintikka and Sandu and Vaananen, and their compositional
semantics due to Hodges. We show how Hodges' semantics can be seen as a special
case of a general construction, which provides a context for a useful
completeness theorem with respect to a wider class of models. We shed some new
light on each aspect of the logic. We show that the natural propositional logic
carried by the semantics is the logic of Bunched Implications due to Pym and
O'Hearn, which combines intuitionistic and multiplicative connectives. This
introduces several new connectives not previously considered in logics of
informational dependence, but which we show play a very natural role, most
notably intuitionistic implication. As regards the quantifiers, we show that
their interpretation in the Hodges semantics is forced, in that they are the
image under the general construction of the usual Tarski semantics; this
implies that they are adjoints to substitution, and hence uniquely determined.
As for the dependence predicate, we show that this is definable from a simpler
predicate, of constancy or dependence on nothing. This makes essential use of
the intuitionistic implication. The Armstrong axioms for functional dependence
are then recovered as a standard set of axioms for intuitionistic implication.
We also prove a full abstraction result in the style of Hodges, in which the
intuitionistic implication plays a very natural r\^ole.Comment: 28 pages, journal versio
Constrained Query Answering
Traditional answering methods evaluate queries only against positive
and definite knowledge expressed by means of facts and deduction rules. They do
not make use of negative, disjunctive or existential information. Negative or indefinite
knowledge is however often available in knowledge base systems, either as
design requirements, or as observed properties. Such knowledge can serve to rule out
unproductive subexpressions during query answering. In this article, we propose an
approach for constraining any conventional query answering procedure with general,
possibly negative or indefinite formulas, so as to discard impossible cases and to
avoid redundant evaluations. This approach does not impose additional conditions
on the positive and definite knowledge, nor does it assume any particular semantics
for negation. It adopts that of the conventional query answering procedure it
constrains. This is achieved by relying on meta-interpretation for specifying the
constraining process. The soundness, completeness, and termination of the underlying
query answering procedure are not compromised. Constrained query answering
can be applied for answering queries more efficiently as well as for generating more
informative, intensional answers
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