scholarly journals Reasoning About the Transfer of Control

2010 ◽  
Vol 37 ◽  
pp. 437-477 ◽  
Author(s):  
W. Van der Hoek ◽  
D. Walther ◽  
M. Wooldridge
Keyword(s):  
Computational Complexity ◽  
Model Checking ◽  
Dynamic Logic ◽  
Second Order ◽  
Kripke Semantics ◽  
Alternative Semantics ◽  
Form Complex ◽  
Transfer Programs ◽  
First Order ◽  
State Of Affairs

We present DCL-PC: a logic for reasoning about how the abilities of agents and coalitions of agents are altered by transferring control from one agent to another. The logical foundation of DCL-PC is CL-PC, a logic for reasoning about cooperation in which the abilities of agents and coalitions of agents stem from a distribution of atomic Boolean variables to individual agents -- the choices available to a coalition correspond to assignments to the variables the coalition controls. The basic modal constructs of DCL-PC are of the form `coalition C can cooperate to bring about phi'. DCL-PC extends CL-PC with dynamic logic modalities in which atomic programs are of the form `agent i gives control of variable p to agent j'; as usual in dynamic logic, these atomic programs may be combined using sequence, iteration, choice, and test operators to form complex programs. By combining such dynamic transfer programs with cooperation modalities, it becomes possible to reason about how the power of agents and coalitions is affected by the transfer of control. We give two alternative semantics for the logic: a `direct' semantics, in which we capture the distributions of Boolean variables to agents; and a more conventional Kripke semantics. We prove that these semantics are equivalent, and then present an axiomatization for the logic. We investigate the computational complexity of model checking and satisfiability for DCL-PC, and show that both problems are PSPACE-complete (and hence no worse than the underlying logic CL-PC). Finally, we investigate the characterisation of control in DCL-PC. We distinguish between first-order control -- the ability of an agent or coalition to control some state of affairs through the assignment of values to the variables under the control of the agent or coalition -- and second-order control -- the ability of an agent to exert control over the control that other agents have by transferring variables to other agents. We give a logical characterisation of second-order control.

scholarly journals Dynamic Logic for Data-aware Systems: Decidability Results

2017 ◽  
Author(s):  
Francesco Belardinelli ◽  
Andreas Herzig
Keyword(s):  
Model Checking ◽  
Dynamic Logic ◽  
English Auctions ◽  
First Order ◽  
Formal Framework ◽  
Data Content ◽  
Order Extension

We introduce a first-order extension of dynamic logic (FO-DL), suitable to represent and reason about the behaviour of Data-aware Systems (DaS), which are systems whose data content is explicitly exhibited in the system’s description. We illustrate the expressivity of the formal framework by modelling English auctions as DaS, and by specifying relevant properties in FO-DL. Most importantly, we develop an abstraction-based verification procedure, thus proving that the model checking problem for DaS against FO-DL is actually decidable, provided some mild assumptions on the interpretationdomain.

Predicate calculus

2018 ◽  
Author(s):  
Timothy Smiley
Keyword(s):  
Propositional Calculus ◽  
Second Order ◽  
Order Logic ◽  
Predicate Calculus ◽  
First Order Logic ◽  
Complex Predicates ◽  
Modern Logic ◽  
Form Complex ◽  
First Order ◽  
Second Order Logic

The predicate calculus is the dominant system of modern logic, having displaced the traditional Aristotelian syllogistic logic that had been the previous paradigm. Like Aristotle’s, it is a logic of quantifiers – words like ‘every’, ‘some’ and ‘no’ that are used to express that a predicate applies universally or with some other distinctive kind of generality, for example ‘everyone is mortal’, ‘someone is mortal’, ‘no one is mortal’. The weakness of syllogistic logic was its inability to represent the structure of complex predicates. Thus it could not cope with argument patterns like ‘everything Fs and Gs, so everything Fs’. Nor could it cope with relations, because a logic of relations must be able to analyse cases where a quantifier is applied to a predicate that already contains one, as in ‘someone loves everyone’. Remedying the weakness required two major innovations. One was a logic of connectives – words like ‘and’, ‘or’ and ‘if’ that form complex sentences out of simpler ones. It is often studied as a distinct system: the propositional calculus. A proposition here is a true-or-false sentence and the guiding principle of propositional calculus is truth-functionality, meaning that the truth-value (truth or falsity) of a compound proposition is uniquely determined by the truth-values of its components. Its principal connectives are negation, conjunction, disjunction and a ‘material’ (that is, truth-functional) conditional. Truth-functionality makes it possible to compute the truth-values of propositions of arbitrary complexity in terms of their basic propositional constituents, and so develop the logic of tautology and tautological consequence (logical truth and consequence in virtue of the connectives). The other invention was the quantifier-variable notation. Variables are letters used to indicate things in an unspecific way; thus ‘x is mortal’ is read as predicating of an unspecified thing x what ‘Socrates is mortal’ predicates of Socrates. The connectives can now be used to form complex predicates as well as propositions, for example ‘x is human and x is mortal’; while different variables can be used in different places to express relational predicates, for example ‘x loves y’. The quantifier goes in front of the predicate it governs, with the relevant variable repeated beside it to indicate which positions are being generalized. These radical departures from the idiom of quantification in natural languages are needed to solve the further problem of ambiguity of scope. Compare, for example, the ambiguity of ‘someone loves everyone’ with the unambiguous alternative renderings ‘there is an x such that for every y, x loves y’ and ‘for every y, there is an x such that x loves y’. The result is a pattern of formal language based on a non-logical vocabulary of names of things and primitive predicates expressing properties and relations of things. The logical constants are the truth-functional connectives and the universal and existential quantifiers, plus a stock of variables construed as ranging over things. This is ‘the’ predicate calculus. A common option is to add the identity sign as a further logical constant, producing the predicate calculus with identity. The first modern logic of quantification, Frege’s of 1879, was designed to express generalizations not only about individual things but also about properties of individuals. It would nowadays be classified as a second-order logic, to distinguish it from the first-order logic described above. Second-order logic is much richer in expressive power than first-order logic, but at a price: first-order logic can be axiomatized, second-order logic cannot.

scholarly journals Abstract Interpretation in the Operational Semantics Hierarchy

1997 ◽  
Vol 4 (2) ◽  
Author(s):  
David A. Schmidt
Keyword(s):  
Model Checking ◽  
Abstract Interpretation ◽  
Data Flow ◽  
Flow Analysis ◽  
Operational Semantics ◽  
Second Order ◽  
Analysis Model ◽  
Small Step ◽  
Data Flow Analysis ◽  
First Order

We systematically apply the principles of Cousot-Cousot-style abstract interpretation (a.i.) to the hierarchy of operational semantics definitions - flowchart, big-step, and small-step semantics. For each semantics format we examine the principles of safety and liveness interpretations, first-order and second-order analyses, and termination properties. Application of a.i. to data-flow analysis, model checking, closure analysis, and concurrency theory are demonstrated. Our primary contributions are separating the concerns of safety, termination, and efficiency of representation and showing how a.i. principles apply uniformly to the various levels of the operational semantics hierarchy and their applications.

How to glue analysis models

1984 ◽  
Vol 49 (4) ◽  
pp. 1339-1349 ◽  
Author(s):  
D. Van Dalen
Keyword(s):  
Intuitionistic Logic ◽  
Second Order ◽  
Kripke Semantics ◽  
Kripke Models ◽  
Closure Properties ◽  
Second Order Arithmetic ◽  
First Order ◽  
Order Arithmetic ◽  
Analysis Models

Among the more traditional semantics for intuitionistic logic the Beth and the Kripke semantics seem well-suited for direct manipulations required for the derivation of metamathematical results. In particular Smoryński demonstrated the usefulness of Kripke models for the purpose of obtaining closure properties for first-order arithmetic, [S], and second-order arithmetic, [J-S]. Weinstein used similar techniques to handle intuitionistic analysis, [W]. Since, however, Beth-models seem to lend themselves better for dealing with analysis, cf. [D], we have developed a somewhat more liberal semantics, that shares the features of both Kripke and Beth semantics, in order to obtain analogues of Smoryński's collecting operations, which we will call Smoryński-glueing, in line with the categorical tradition.

Nonlinear Analysis of Visual Evoked Potentials Elicited by Color Stimulation

1997 ◽  
Vol 36 (04/05) ◽  
pp. 315-318 ◽  
Author(s):  
K. Momose ◽  
K. Komiya ◽  
A. Uchiyama
Keyword(s):  
Visual System ◽  
Evoked Potentials ◽  
Visual Evoked Potentials ◽  
Normal Subjects ◽  
Second Order ◽  
First Order ◽  
The Relationship ◽  
Perceived Color ◽  
Second Order Nonlinearity ◽  
Visual Evoked

Abstract:The relationship between chromatically modulated stimuli and visual evoked potentials (VEPs) was considered. VEPs of normal subjects elicited by chromatically modulated stimuli were measured under several color adaptations, and their binary kernels were estimated. Up to the second-order, binary kernels obtained from VEPs were so characteristic that the VEP-chromatic modulation system showed second-order nonlinearity. First-order binary kernels depended on the color of the stimulus and adaptation, whereas second-order kernels showed almost no difference. This result indicates that the waveforms of first-order binary kernels reflect perceived color (hue). This supports the suggestion that kernels of VEPs include color responses, and could be used as a probe with which to examine the color visual system.

Imaginings

2017 ◽  
Vol 9 (3) ◽  
pp. 17-30
Author(s):  
Kelly James Clark
Keyword(s):  
Religious Tradition ◽  
Second Order ◽  
Fine Tuning ◽  
Intellectual Humility ◽  
First Order ◽  
Natural Processes ◽  
Empirically Supported ◽  
Group Violence ◽  
The World ◽  
The Universe

In Branden Thornhill-Miller and Peter Millican’s challenging and provocative essay, we hear a considerably longer, more scholarly and less melodic rendition of John Lennon’s catchy tune—without religion, or at least without first-order supernaturalisms (the kinds of religion we find in the world), there’d be significantly less intra-group violence. First-order supernaturalist beliefs, as defined by Thornhill-Miller and Peter Millican (hereafter M&M), are “beliefs that claim unique authority for some particular religious tradition in preference to all others” (3). According to M&M, first-order supernaturalist beliefs are exclusivist, dogmatic, empirically unsupported, and irrational. Moreover, again according to M&M, we have perfectly natural explanations of the causes that underlie such beliefs (they seem to conceive of such natural explanations as debunking explanations). They then make a case for second-order supernaturalism, “which maintains that the universe in general, and the religious sensitivities of humanity in particular, have been formed by supernatural powers working through natural processes” (3). Second-order supernaturalism is a kind of theism, more closely akin to deism than, say, Christianity or Buddhism. It is, as such, universal (according to contemporary psychology of religion), empirically supported (according to philosophy in the form of the Fine-Tuning Argument), and beneficial (and so justified pragmatically). With respect to its pragmatic value, second-order supernaturalism, according to M&M, gets the good(s) of religion (cooperation, trust, etc) without its bad(s) (conflict and violence). Second-order supernaturalism is thus rational (and possibly true) and inconducive to violence. In this paper, I will examine just one small but important part of M&M’s argument: the claim that (first-order) religion is a primary motivator of violence and that its elimination would eliminate or curtail a great deal of violence in the world. Imagine, they say, no religion, too.Janusz Salamon offers a friendly extension or clarification of M&M’s second-order theism, one that I think, with emendations, has promise. He argues that the core of first-order religions, the belief that Ultimate Reality is the Ultimate Good (agatheism), is rational (agreeing that their particular claims are not) and, if widely conceded and endorsed by adherents of first-order religions, would reduce conflict in the world.While I favor the virtue of intellectual humility endorsed in both papers, I will argue contra M&M that (a) belief in first-order religion is not a primary motivator of conflict and violence (and so eliminating first-order religion won’t reduce violence). Second, partly contra Salamon, who I think is half right (but not half wrong), I will argue that (b) the religious resources for compassion can and should come from within both the particular (often exclusivist) and the universal (agatheistic) aspects of religious beliefs. Finally, I will argue that (c) both are guilty, as I am, of the philosopher’s obsession with belief. 

Evidence for general base catalysis by protic solvents in a kinetic study of alcoholyses and hydrolyses of 1-(phenoxycarbonyl)pyridinium ions under both solvolytic and non-solvolytic conditions

2009 ◽  
Vol 74 (1) ◽  
pp. 43-55 ◽  
Author(s):  
Dennis N. Kevill ◽  
Byoung-Chun Park ◽  
Jin Burm Kyong
Keyword(s):  
Second Order ◽  
Base Catalysis ◽  
Substitution Reactions ◽  
Third Order ◽  
Methoxy Derivative ◽  
First Order ◽  
General Base ◽  
Protic Solvents ◽  
Kinetics Of ◽  
Pyridinium Ions

The kinetics of nucleophilic substitution reactions of 1-(phenoxycarbonyl)pyridinium ions, prepared with the essentially non-nucleophilic/non-basic fluoroborate as the counterion, have been studied using up to 1.60 M methanol in acetonitrile as solvent and under solvolytic conditions in 2,2,2-trifluoroethan-1-ol (TFE) and its mixtures with water. Under the non- solvolytic conditions, the parent and three pyridine-ring-substituted derivatives were studied. Both second-order (first-order in methanol) and third-order (second-order in methanol) kinetic contributions were observed. In the solvolysis studies, since solvent ionizing power values were almost constant over the range of aqueous TFE studied, a Grunwald–Winstein equation treatment of the specific rates of solvolysis for the parent and the 4-methoxy derivative could be carried out in terms of variations in solvent nucleophilicity, and an appreciable sensitivity to changes in solvent nucleophilicity was found.

Metaontology

2018 ◽  
Author(s):  
Uriah Kriegel
Keyword(s):  
Second Order ◽  
Order Property ◽  
First Order ◽  
First Approximation

Brentano’s theory of judgment serves as a springboard for his conception of reality, indeed for his ontology. It does so, indirectly, by inspiring a very specific metaontology. To a first approximation, ontology is concerned with what exists, metaontology with what it means to say that something exists. So understood, metaontology has been dominated by three views: (i) existence as a substantive first-order property that some things have and some do not, (ii) existence as a formal first-order property that everything has, and (iii) existence as a second-order property of existents’ distinctive properties. Brentano offers a fourth and completely different approach to existence talk, however, one which falls naturally out of his theory of judgment. The purpose of this chapter is to present and motivate Brentano’s approach.

Categoricity and the sets

2018 ◽  
Author(s):  
Tim Button ◽  
Sean Walsh
Keyword(s):  
Set Theory ◽  
Second Order ◽  
Order Logic ◽  
First Order ◽  
The Status ◽  
Second Order Logic ◽  
Philosophy Of Set Theory ◽  
Order Set

In this chapter, the focus shifts from numbers to sets. Again, no first-order set theory can hope to get anywhere near categoricity, but Zermelo famously proved the quasi-categoricity of second-order set theory. As in the previous chapter, we must ask who is entitled to invoke full second-order logic. That question is as subtle as before, and raises the same problem for moderate modelists. However, the quasi-categorical nature of Zermelo's Theorem gives rise to some specific questions concerning the aims of axiomatic set theories. Given the status of Zermelo's Theorem in the philosophy of set theory, we include a stand-alone proof of this theorem. We also prove a similar quasi-categoricity for Scott-Potter set theory, a theory which axiomatises the idea of an arbitrary stage of the iterative hierarchy.

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