194 research outputs found
Concurrent Kleene Algebra: Free Model and Completeness
Concurrent Kleene Algebra (CKA) was introduced by Hoare, Moeller, Struth and
Wehrman in 2009 as a framework to reason about concurrent programs. We prove
that the axioms for CKA with bounded parallelism are complete for the semantics
proposed in the original paper; consequently, these semantics are the free
model for this fragment. This result settles a conjecture of Hoare and
collaborators. Moreover, the techniques developed along the way are reusable;
in particular, they allow us to establish pomset automata as an operational
model for CKA.Comment: Version 2 includes an overview section that outlines the completeness
proof, as well as some extra discussion of the interpolation lemma. It also
includes better typography and a number of minor fixes. Version 3
incorporates the changes by comments from the anonymous referees at ESOP.
Among other things, these include a worked example of computing the syntactic
closure by han
On Semantic Gamification
The purpose of this essay is to study the extent in which the semantics for different logical systems can be represented game theoretically. I will begin by considering different definitions of what it means to gamify a semantics, and show completeness and limitative results. In particular, I will argue that under a proper definition of gamification, all finitely algebraizable logics can be gamified, as well as some infinitely algebraizable ones (like Ćukasiewicz) and some non-algebraizable (like intuitionistic and van Fraassen supervaluation logic)
Field's Logic of Truth
Saving Truth from Paradox is a re-exciting development. The 70s and 80s were a time of excitement among people working on the semantic paradoxes. There were continual formal developments, with the constant hope that these results would yield deep insights. The enthusiasm wore off, however, as people became more cognizant of the disparity between what they had accomplished, impressive as it was, and what they had hoped to accomplish. They moved onto other problems that they hoped would prove more yielding. That, at least, was how it seemed to me, so I was delighted to see a dramatically new formal development that is likely to rekindle our enthusiasm
The KB paradigm and its application to interactive configuration
The knowledge base paradigm aims to express domain knowledge in a rich formal
language, and to use this domain knowledge as a knowledge base to solve various
problems and tasks that arise in the domain by applying multiple forms of
inference. As such, the paradigm applies a strict separation of concerns
between information and problem solving. In this paper, we analyze the
principles and feasibility of the knowledge base paradigm in the context of an
important class of applications: interactive configuration problems. In
interactive configuration problems, a configuration of interrelated objects
under constraints is searched, where the system assists the user in reaching an
intended configuration. It is widely recognized in industry that good software
solutions for these problems are very difficult to develop. We investigate such
problems from the perspective of the KB paradigm. We show that multiple
functionalities in this domain can be achieved by applying different forms of
logical inferences on a formal specification of the configuration domain. We
report on a proof of concept of this approach in a real-life application with a
banking company. To appear in Theory and Practice of Logic Programming (TPLP).Comment: To appear in Theory and Practice of Logic Programming (TPLP
Enhanced Graph Rewriting Systems for Complex Software Domain
International audienceMethodologies for correct by construction reconfigurations can efficiently solve consistency issues in dynamic software architecture. Graph-based models are appropriate for designing such architectures and methods. At the same time, they may be unfit to characterize a system from a non functional perspective. This stems from efficiency and applicability limitations in handling time-varying characteristics and their related dependencies. In order to lift these restrictions, an extension to graph rewriting systems is proposed herein. The suitability of this approach, as well as the restraints of currently available ones, are illustrated, analysed and experimentally evaluated with reference to a concrete example. This investigation demonstrates that the conceived solution can: (i) express any kind of algebraic dependencies between evolving requirements and properties; (ii) significantly ameliorate the efficiency and scalability of system modifications with respect to classic methodologies; (iii) provide an efficient access to attribute values; (iv) be fruitfully exploited in software management systems; (v) guarantee theoretical properties of a grammar, like its termination
Change Actions: Models of Generalised Differentiation
Cai et al. have recently proposed change structures as a semantic framework
for incremental computation. We generalise change structures to arbitrary
cartesian categories and propose the notion of change action model as a
categorical model for (higher-order) generalised differentiation. Change action
models naturally arise from many geometric and computational settings, such as
(generalised) cartesian differential categories, group models of discrete
calculus, and Kleene algebra of regular expressions. We show how to build
canonical change action models on arbitrary cartesian categories, reminiscent
of the F\`aa di Bruno construction
Multiple Conclusion Rules in Logics with the Disjunction Property
We prove that for the intermediate logics with the disjunction property any
basis of admissible rules can be reduced to a basis of admissible m-rules
(multiple-conclusion rules), and every basis of admissible m-rules can be
reduced to a basis of admissible rules. These results can be generalized to a
broad class of logics including positive logic and its extensions, Johansson
logic, normal extensions of S4, n-transitive logics and intuitionistic modal
logics
Measuring the intelligence of an idealized mechanical knowing agent
We define a notion of the intelligence level of an idealized mechanical knowing agent. This is motivated by efforts within artificial intelligence research to define real-number intelligence levels of compli- cated intelligent systems. Our agents are more idealized, which allows us to define a much simpler measure of intelligence level for them. In short, we define the intelligence level of a mechanical knowing agent to be the supremum of the computable ordinals that have codes the agent knows to be codes of computable ordinals. We prove that if one agent knows certain things about another agent, then the former necessarily has a higher intelligence level than the latter. This allows our intelligence no- tion to serve as a stepping stone to obtain results which, by themselves, are not stated in terms of our intelligence notion (results of potential in- terest even to readers totally skeptical that our notion correctly captures intelligence). As an application, we argue that these results comprise evidence against the possibility of intelligence explosion (that is, the no- tion that sufficiently intelligent machines will eventually be capable of designing even more intelligent machines, which can then design even more intelligent machines, and so on)
Soundness and completeness proofs by coinductive methods
We show how codatatypes can be employed to produce compact, high-level proofs of key results in logic: the soundness and completeness of proof systems for variations of first-order logic. For the classical completeness result, we first establish an abstract property of possibly infinite derivation trees. The abstract proof can be instantiated for a wide range of Gentzen and tableau systems for various flavors of first-order logic. Soundness becomes interesting as soon as one allows infinite proofs of first-order formulas. This forms the subject of several cyclic proof systems for first-order logic augmented with inductive predicate definitions studied in the literature. All the discussed results are formalized using Isabelle/HOLâs recently introduced support for codatatypes and corecursion. The development illustrates some unique features of Isabelle/HOLâs new coinductive specification language such as nesting through non-free types and mixed recursionâcorecursion
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