Atomic Predicate Research Articles

Optimal Control of Colored Timed Petri Nets Under Generalized Mutual Exclusion Temporal Constraints

A coloured Petri net (CPN) is widely used to model discrete event systems due to its compact representation of the system by colour sets associated with places, transitions and I/O arcs. For real-world systems such as manufacturing systems, transportation systems, and communication protocols, a coloured timed Petri net (CTPN) is proposed to model timed behaviours. To control a discrete event system with a desired control specification, it is important to describe the control specification formally. For the CPN, a class of specification called coloured generalized mutual exclusion constraints (cGMEC) is utilized to specify the behaviours. However, cGMEC can only represent safety constraints and not temporal constraints. Therefore, in this paper, we propose a novel temporal logic based constraint called a coloured generalized mutual exclusion temporal constraint (cGMETC). The cGMETC is described by a signal temporal logic (STL) formula where each atomic predicate represents a cGMEC. We propose a method for optimal control of the CTPN under a given cGMETC. In particular, we formulate an optimal control problem and solve the problem by transforming it into an integer linear programming problem. Through a simulation of an optimal control problem of a manufacturing system, we demonstrate the effectiveness of the proposed approach.

How Category Selection Impacts Inference Reliability: Inheritance Inference From an Ecological Perspective

This article presents results from a simulation-based study of inheritance inference, that is, inference from the typicality of a property among a "base" class to its typicality among a subclass of the class. The study aims to ascertain which kinds of inheritance inferences are reliable, with attention to the dependence of their reliability upon the type of environment in which inferences are made. For example, the study addresses whether inheritance inference is reliable in the case of "exceptional subclasses" (i.e., subclasses that are known to be atypical in some respect) and attends to variations in reliability that result from variations in the entropy level of the environment. A further goal of the study is to show that the reliability of inheritance inference depends crucially on which sorts of base classes are used in making inferences. One approach to inheritance inference treats the extension of any atomic predicate as a suitable base class. A second approach identifies suitable base classes with the cells of a partition (of a preselected size k) of the domain of objects that satisfies the condition of maximizing the similarity of objects that are assigned to the same class. In addition to permitting more inferences, our study shows that the second approach results in inheritance inferences that are far more reliable, particularly in the case of exceptional subclasses.

O singular nu no inglês e no português brasileiro: abordagens experimentais sobre atomicidade

A partir de uma discussão sobre o papel da atomicidade no domínio da distinção contável-massivo, propomos uma análise para o Singular Nu (SNU) tanto no inglês quanto no português brasileiro (PB). Nosso objetivo é verificar experimentalmente o caráter atômico (ou não) desses sintagmas. Para tanto, analisamos dados de um teste realizado por Scontras, Davidson, Deal e Murray (2017), que mostram que o SNU no inglês enseja principalmente leitura de volume em comparativas. Segundo nossa análise, essa interpretação é explicada como coerção, o que corrobora a denotação do SNU como um predicado atômico nessa língua. Para o caso do SNU no PB, desenvolvemos um teste de julgamento de quantidade, nos moldes de Scontras et al.(2017), para verificar as dimensões usadas na comparação em sentenças com o plural, o nome massivo e o SNU, em oposição a sentenças sem o nome expresso (Quem tem mais?). Os resultados mostram que sentenças com o SNU possuem os mesmos julgamentos de sentenças sem o nome expresso. Argumentamos, então, que o SNU no PB não carrega qualquer traço gramatical de atomicidade, diferentemente do plural e do nome massivo, que carregam traços [+atom] e [-atom] respetivamente.

Real-Time Verification of Network Properties Using Atomic Predicates

Network management will benefit from automated tools based upon formal methods. Several such tools have been published in the literature. We present a new formal method for a new tool, Atomic Predicates (AP) Verifier, which is much more time and space efficient than existing tools. Given a set of predicates representing packet filters, AP Verifier computes a set of atomic predicates, which is minimum and unique. The use of atomic predicates dramatically speeds up computation of network reachability. We evaluated the performance of AP Verifier using forwarding tables and ACLs from three large real networks. The atomic predicate sets of these networks were computed very quickly and their sizes are surprisingly small. Real networks are subject to dynamic state changes over time as a result of rule insertion and deletion by protocols and operators, failure and recovery of links and boxes, etc. In a software-defined network, the network state can be observed in real time and thus may be controlled in real time. AP Verifier includes algorithms to process such events and check compliance with network policies and properties in real time. We compare time and space costs of AP Verifier with Header Space and NetPlumber using datasets from the real networks.

Guarded Negation

We consider restrictions of first-order logic and of fixpoint logic in which all occurrences of negation are required to be guarded by an atomic predicate. In terms of expressive power, the logics in question, called GNFO and GNFP, extend the guarded fragment of first-order logic and the guarded least fixpoint logic, respectively. They also extend the recently introduced unary negation fragments of first-order logic and of least fixpoint logic. We show that the satisfiability problem for GNFO and for GNFP is 2ExpTime-complete, both on arbitrary structures and on finite structures. We also study the complexity of the associated model checking problems. Finally, we show that GNFO and GNFP are not only computationally well behaved, but also model theoretically: we show that GNFO and GNFP have the tree-like model property and that GNFO has the finite model property, and we characterize the expressive power of GNFO in terms of invariance for an appropriate notion of bisimulation. Our complexity upper bounds for GNFO and GNFP hold true even for their “clique-guarded” extensions CGNFO and CGNFP, in which clique guards are allowed in the place of guards.

Construction of logic and linguistic models of typical natural language structures

As simple sentence in formal logic is an atomic predicate, the complex (compound) sentence is a complex logical expression, set of atomic predicates combined logical connectives. The logic and linguistic model is exactly a relationship between elements of formal logic and syntactic structure of natural language sentences. The analysis of natural language sentences revealed conceptual attitude, control and fit, based on what it was formed the logic and linguistic model of functional relationships. The article discovered possible types of relations in natural language sentences that appear in logic and linguistic models using logical operations of conjunction, disjunction and implication. The article suggests a generalized form of logic and linguistic model; it derives logic and linguistic model’s typical templates for specific types of natural language sentences. Depending on the conceptual relations between simple sentences that are parts of a complex one, logic and linguistic model’s parts are interpreted as complex or simple expressions that allow to return recursively to the general form of the formula and to apply it to the specific situation until all the parts of natural language sentence of are clearly interpreted.

Approximating the limit: the interaction between quasi ‘almost’ and some temporal connectives in Italian

This paper focuses on the interpretation of the Italian approximative adverb quasi ‘almost’ by primarily looking at cases in which it modifies temporal connectives, a domain which, to our knowledge, has been largely unexplored thus far. Consideration of this domain supports the need for a scalar account of the semantics of quasi (close in spirit to Hitzeman’s semantic analysis of almost, in: Canakis et al. (eds) Papers from the 28th regional meeting of the Chicago Linguistic Society, 1992). When paired with suitable analyses of temporal connectives, such an account can provide a simple explanation of the patterns of implication that are observed when quasi modifies locational (e.g. quando ‘when’), directional (e.g. fino ‘until’ and da ‘since’), and event-sequencing temporal connectives (e.g. prima ‘before’ and dopo ‘after’). A challenging empirical phenomenon that is observed is a contrast between the modification of fino and da by quasi, on the one hand, and the modification of prima and dopo by the same adverb, on the other. While quasi fino and quasi da behave symmetrically, a puzzling asymmetry is observed between quasi prima and quasi dopo. To explain the asymmetry, we propose an analysis of prima and dopo on which the former has the meaning of the temporal comparative piu presto ‘earlier’, while the latter is seen as an atomic predicate denoting temporal succession between events (Del Prete, Nat Lang Semantics 16:157–203, 2008). We show that the same pattern of implication observed for quasi prima is attested when quasi modifies overt comparatives, and propose a pragmatic analysis of this pattern that uniformly applies to both cases, thus providing new evidence for the claim that prima is underlyingly a comparative. A major point of this paper is a discussion of the notion of scale which is relevant for the semantics of quasi; in particular, we show that the notion of Horn (entailment-based) scale is not well-suited for handling modification of temporal connectives, and that a more general notion of scale is required in order to provide a uniform analysis of quasi as a cross-categorial modifier.

A common axiom set for classical and intuitionistic plane geometry

We describe a first order axiom set which yields the classical first order Euclidean geometry of Tarski when used with classical logic, and yields an intuitionistic (or constructive) Euclidean geometry when used with intuitionistic logic. The first order language has a single six place atomic predicate and no function symbols. The intuitionistic system has a computational interpretation in recursive function theory, that is, a realizability interpretation analogous to those given by Kleene for intuitionistic arithmetic and analysis. This interpretation shows the unprovability in the intuitionistic theory of certain “nonconstructive” theorems of the classical geometry.

Forcing and the indeterminacy of translation

Quine has argued1 that the indeterminacy of translation is a more general phenomenon than the inscrutability of reference, the latter being but one pillar that supports the former. What Quine has in mind is clearly this. The thesis of inscrutability of reference is the claim that a referring term t can, faithfully to all data about the occasions of its use, be set equivalen to two referring terms t' and t" that are not codesignative. All three terms may belong to the same language; but it is heuristically effective to think of t' and t" as translations off. The indeterminacy of translation holds that there can be two translations S' and S" of a sentence S, both faithful to all data about the occasions of use of S, such that 5" is obviously inequivalent to S". (In some cases, of course, S' will be materially equivalent to S'f.) Again, all three sentences may belong to the same language, but it is helpful to think of S' and S" as competing translations of S into another language. The two theses, then, are not synonymous. It is clear that inscrutability entails indeterminacy. To see this, suppose a translation were determinate in respect of everything but terms. Thus if S(t) is a sentence in which a term t occurs, let it be assumed that there is only one possible translation of the open sentence S(...): call it S'(...). Still, S(t) can be translated as either S'(t') or S'(t"), which by the second part of our supposition will in general be inequivalent in any sense of equivalence stronger than agreement in truth value. ("In general," because this may not go through for all choices of S(...). For example, suppose S(...) is translated as 2 + 2 = 4 v = . Clearly (2 + 2 = 4 v t' = /') = (2 + 2 = 4 v t" = t") = 2 + 2 = 4, so here S'(t') is strongly equivalent to S'(t"). To guard against such cases, we may suppose S'(...) to be an atomic observation predicate.) What one would like to see, per Quine's claim, is a convincing case of translational indeterminacy that does not depend on inscrutability in this way preferably a case of translational indeterminacy which does not explicitly involve the interpretation of terms at all, and throughout which the interpretation of terms can be held constant. This need is especially pressing if one has doubts about the