47,265 research outputs found
Admissibility in Finitely Generated Quasivarieties
Checking the admissibility of quasiequations in a finitely generated (i.e.,
generated by a finite set of finite algebras) quasivariety Q amounts to
checking validity in a suitable finite free algebra of the quasivariety, and is
therefore decidable. However, since free algebras may be large even for small
sets of small algebras and very few generators, this naive method for checking
admissibility in \Q is not computationally feasible. In this paper,
algorithms are introduced that generate a minimal (with respect to a multiset
well-ordering on their cardinalities) finite set of algebras such that the
validity of a quasiequation in this set corresponds to admissibility of the
quasiequation in Q. In particular, structural completeness (validity and
admissibility coincide) and almost structural completeness (validity and
admissibility coincide for quasiequations with unifiable premises) can be
checked. The algorithms are illustrated with a selection of well-known finitely
generated quasivarieties, and adapted to handle also admissibility of rules in
finite-valued logics
The Return of Noncongruent Equal Protection
Contemporary equal protection doctrine touts the principle of congruence: the notion that equal protection means the same thing whether applied to state or to federal laws. The federalism-tinged equal protection analysis at the heart of Justice Kennedyâs opinion in United States v. Windsor, however, necessarily violates the congruence principle. Commentators and courtsâespecially those deciding how Windsorâs federalism should affect the ever-growing number of state same-sex marriage casesâhave so far failed to account for Windsorâs noncongruent equal protection, much less ask whether noncongruence is generally desirable, and if so, what form it should take. This Article draws answers to those questions from the Supreme Courtâs alienage discrimination cases, which offer three distinct models of noncongruence, each of which is reflected in Windsor. The alienage cases show that instead of applying different levels of scrutiny to federal and state laws, a better understanding of noncongruence would allow different levels of government to assert different interests in defending their laws. By reconstructing and evaluating the ways that structure and rights intersect in the alienage cases, this Article considers for the first time what the return of noncongruent equal protection could mean both for cases that follow Windsor and for equal protection doctrine more broadly
States in Process Calculi
Formal reasoning about distributed algorithms (like Consensus) typically
requires to analyze global states in a traditional state-based style. This is
in contrast to the traditional action-based reasoning of process calculi.
Nevertheless, we use domain-specific variants of the latter, as they are
convenient modeling languages in which the local code of processes can be
programmed explicitly, with the local state information usually managed via
parameter lists of process constants. However, domain-specific process calculi
are often equipped with (unlabeled) reduction semantics, building upon a rich
and convenient notion of structural congruence. Unfortunately, the price for
this convenience is that the analysis is cumbersome: the set of reachable
states is modulo structural congruence, and the processes' state information is
very hard to identify. We extract from congruence classes of reachable states
individual state-informative representatives that we supply with a proper
formal semantics. As a result, we can now freely switch between the process
calculus terms and their representatives, and we can use the stateful
representatives to perform assertional reasoning on process calculus models.Comment: In Proceedings EXPRESS/SOS 2014, arXiv:1408.127
On Observing Dynamic Prioritised Actions in SOC
We study the impact on observational semantics for SOC of priority mechanisms which combine dynamic priority with local pre-emption. We define manageable notions of strong and weak labelled bisimilarities for COWS, a process calculus for SOC, and provide alternative characterisations in terms of open barbed bisimilarities. These semantics show that COWSâs priority mechanisms partially recover the capability to observe receive actions (that could not be observed in a purely asynchronous setting) and that high priority primitives for termination impose specific conditions on the bisimilarities
Oppressive Things
In analyzing oppressive systems like racism, social theorists have articulated accounts of the dynamic interaction and mutual dependence between psychological components, such as individualsâ patterns of thought and action, and social components, such as formal institutions and informal interactions. We argue for the further inclusion of physical components, such as material artifacts and spatial environments. Drawing on socially situated and ecologically embedded approaches in the cognitive sciences, we argue that physical components of racism are not only shaped by, but also shape psychological and social components of racism. Indeed, while our initial focus is on racism and racist things, we contend that our framework is also applicable to other oppressive systems, including sexism, classism, and ableism. This is because racist things are part of a broader class of oppressive things, which are material artifacts and spatial environments that are in congruence with an oppressive system
Beating the Productivity Checker Using Embedded Languages
Some total languages, like Agda and Coq, allow the use of guarded corecursion
to construct infinite values and proofs. Guarded corecursion is a form of
recursion in which arbitrary recursive calls are allowed, as long as they are
guarded by a coinductive constructor. Guardedness ensures that programs are
productive, i.e. that every finite prefix of an infinite value can be computed
in finite time. However, many productive programs are not guarded, and it can
be nontrivial to put them in guarded form.
This paper gives a method for turning a productive program into a guarded
program. The method amounts to defining a problem-specific language as a data
type, writing the program in the problem-specific language, and writing a
guarded interpreter for this language.Comment: In Proceedings PAR 2010, arXiv:1012.455
The Lattice of Congruences of a Finite Line Frame
Let be a finite Kripke frame. A
congruence of is a bisimulation of that is also an
equivalence relation on F. The set of all congruences of is a
lattice under the inclusion ordering. In this article we investigate this
lattice in the case that is a finite line frame. We give concrete
descriptions of the join and meet of two congruences with a nontrivial upper
bound. Through these descriptions we show that for every nontrivial congruence
, the interval embeds into the lattice of
divisors of a suitable positive integer. We also prove that any two congruences
with a nontrivial upper bound permute.Comment: 31 pages, 11 figures. Expanded intro, conclusions rewritten. New,
less geometrical, proofs of Lemma 19 and (former) Lemma 3
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