Order Predicate Research Articles

LQCD workflow execution framework: Models, provenance and fault-tolerance

Large computing clusters used for scientific processing suffer from systemic failures when operated over long continuous periods for executing workflows. Diagnosing job problems and faults leading to eventual failures in this complex environment is difficult, specifically when the success of an entire workflow might be affected by a single job failure. In this paper, we introduce a model-based, hierarchical, reliable execution framework that encompass workflow specification, data provenance, execution tracking and online monitoring of each workflow task, also referred to as participants. The sequence of participants is described in an abstract parameterized view, which is translated into a concrete data dependency based sequence of participants with defined arguments. As participants belonging to a workflow are mapped onto machines and executed, periodic and on-demand monitoring of vital health parameters on allocated nodes is enabled according to pre-specified rules. These rules specify conditions that must be true pre-execution, during execution and post-execution. Monitoring information for each participant is propagated upwards through the reflex and healing architecture, which consists of a hierarchical network of decentralized fault management entities, called reflex engines. They are instantiated as state machines or timed automatons that change state and initiate reflexive mitigation action(s) upon occurrence of certain faults. We describe how this cluster reliability framework is combined with the workflow execution framework using formal rules and actions specified within a structure of first order predicate logic that enables a dynamic management design that reduces manual administrative workload, and increases cluster-productivity.

Reading the mind of God (without Hebrew lessons): Alston, shared attention, and mystical experience

AbstractAlston's perceptual account of mystical experience fails to show how it is that the sort of predicates that are used to describe God in these experiences could be derived from perception, even though the ascription of matched predicates in the natural order are not derived in the manner Alston has in mind. In contrast, if one looks to research on shared attention between individuals as mediated by mirror neurons, then one can give a perceptual account of mystical experience which draws a tighter connection between what is reported in mystical reports and the most similar reports in the natural order.

Fragmentary structure of global knowledge: constructive processes for interoperability

PurposeThe application of category theory to interoperability to increase understanding of the problems and to facilitate the development of practical tools for their solution.Design/methodology/approachCategory theory is naturally suited to handling interoperability. The use of first order predicate logic in many information systems may be justified through its completeness. However, the work of Gödel shows that such systems are undecidable if they rely on formal systems of number and/or sets. For interoperability dyadic higher order logic is required, which is neither complete nor decidable if based on sets. However, pure category theory is still axiomatic so is also neither complete nor decidable. Applied category theory based on cartesian closed categories for process is natural and is both complete and decidable. Gödel's theorems therefore do not apply.FindingsThe paper finds that composed adjunctions appear particularly well‐suited for modelling interoperability, with composition of distinct functors for mapping across a number of levels and of endofunctors for business process interoperability. The monad/comonad category provides a powerful abstraction of the business process. The development of a tool based on categorial principles written in Haskell may be a way forward but only as an initial set model approach.Originality/valueThis paper applies categorial constructions which permit a natural formal approach to interoperability.

The noun/verb and predicate/argument structures

Previously, establishing a correspondence between the noun/verb and first order predicate logic's predicate/argument structures has been found problematic (Hurford, 2003a,b). The present paper argues that the predicate/argument system of natural language is more complex than that of first order predicate logic, with up to three levels of predicates and arguments and a rule system for generating predicates and arguments and converting predicates to arguments and vice versa. A property of this system is that nouns correspond to linguistic arguments and verbs correspond to linguistic predicates while the scope of linguistic arguments and predicates is not restricted to nouns and verbs. In addition, some particular properties of this system as well as general properties of any predicate/argument structure suggest that linguistic arguments (e.g. nouns) may be evolutionarily more fundamental than linguistic predicates (e.g. verbs). The second part of the paper analyzes this hypothesis, originally proposed by Heine and Kuteva (2002, 2007), and concludes, with a number of new arguments from a variety of domains, that the evidence of linguistic arguments predating linguistic predicates is overwhelming.

Where Our Number Concepts Come From

Where Our Number Concepts Come From

Causal Relevance and heterogeneity of Program Explanations in the face of Explanatory Exclusion

n everyday causal explanations of human behaviour, known generally as ‘folk psychology,’ the causal powers of the mental seem to be taken for granted. Mental properties such as perceptions, beliefs, and desires, are all called upon in causal explanations of events that are deemed intentional. Jaegwon Kim’s exclusion principle has led him to deny mental properties causal efficacy unless they are metaphysically reduced to physical properties, but what of their causal relevance? By giving up the assumption of causally efficacious mental properties, has Kim put into question the explanatory value of explanations with mental descriptions? In other words, if a lower order neurological causal explanation involving a causally efficacious property is at hand, does it make the higher order mental explanation irrelevant and therefore redundant? If we are to save the explanatory importance of higher order predicates, and thus the causal explanations of the special sciences and folk psychology, we need an account of how such properties can be relevant as opposed to irrelevant in causal explanations, even though they may not be causally efficacious. Frank Jackson’s and Philip Pettit’s notion of program explanation tries to do just this. There are two ways to read Kim’s causal exclusion principle, metaphysically as causal exclusion, or epistemologically as causal explanatory exclusion. The explanatory exclusion principle hinders the acceptance of two causal explanations for a single effect unless an acceptable relation exists between the two purported causes. In this paper I will concentrate on the epistemological version of the principle, including Kim’s acceptable relations, and contrast it with a survey of Jackson’s and Pettit’s program explanations. My aim is to discover whether program explanations expound an acceptable relation already covered by Kim or present an additional way of understanding how two causal explanations of the same phenomenon can be accepted. Jackson and Pettit say: “The notion of a programming property does not just explain how an inefficacious property can be relevant to the causation of an event. It also shows how a program explanation can have a significance that remains in the presence of an explanation invoking the corresponding I

Force deployment analysis with generalized grammar

We analyse the key algorithms of data and information fusion from a linguistic point of view, and show that they fall into two paradigms: the primarily syntactic, and the primarily semantic. We propose an alternative grammatical paradigm which exploits the ability of grammar to combine syntactic inference with semantic representation. We generalize the concept of formal generative grammar to include multiple rule classes each having a topology and a base vocabulary. A generalized Chomsky hierarchy is defined. Analysing fusion algorithms in terms of grammatical representations, we find that most (including multiple hypothesis tracking) can be expressed in terms of conventional regular grammars. Situation analysis, however, is commonly attempted using first order predicate logic, which while expressive, is recursively enumerable and so scales badly. We argue that the core issue in situation assessment is force deployment assessment, the extraction and scoring of hypotheses of the force deployment history, each of which is a multiresolution account of the activities, groupings and interactions of force components. The force deployment history represents these relationships at multiple levels of granularity and is expressed over time and space. We provide a grammatical approach for inferring such histories, and show that they can be estimated accurately and scalably. We employ a generalized context-free grammar incorporating both sequence and multiset productions. Elaborating [D. McMichael, G. Jarrad, S. Williams, M. Kennett, Grammatical methods for situation and threat analysis, in: Proceedings of The 8th International Conference on Information Fusion, Philadelphia, PA, 2005], a Generalized Functional Combinatory Categorial Grammar (GFCCG) is described that is both generalized and semantically functional (in that the semantics can be calculated directly from the syntax using a small number of rules). Force deployment modelling and parsing is demonstrated in naval and air defence scenarios. Simulation studies indicate that the method robustly handles the errors introduced by trackers under noisy cluttered conditions. The empirical time complexity of batch force deployment parsing is better than O ( N 1.5 ) , where N is the number of track segments. Force deployment assessments are required in real-time, and we have developed an incremental parser that keeps up with real-time data, and fulfils at Level 2 in the JDL fusion hierarchy the role that trackers fulfil at Level 1.

Causal Relevance and Heterogeneity of Program Explanations in the Face of Explanatory Exclusion

n everyday causal explanations of human behaviour, known generally as ‘folk psychology,’ the causal powers of the mental seem to be taken for granted. Mental properties such as perceptions, beliefs, and desires, are all called upon in causal explanations of events that are deemed intentional. Jaegwon Kim’s exclusion principle has led him to deny mental properties causal efficacy unless they are metaphysically reduced to physical properties, but what of their causal relevance? By giving up the assumption of causally efficacious mental properties, has Kim put into question the explanatory value of explanations with mental descriptions? In other words, if a lower order neurological causal explanation involving a causally efficacious property is at hand, does it make the higher order mental explanation irrelevant and therefore redundant? If we are to save the explanatory importance of higher order predicates, and thus the causal explanations of the special sciences and folk psychology, we need an account of how such properties can be relevant as opposed to irrelevant in causal explanations, even though they may not be causally efficacious. Frank Jackson’s and Philip Pettit’s notion of program explanation tries to do just this. There are two ways to read Kim’s causal exclusion principle, metaphysically as causal exclusion, or epistemologically as causal explanatory exclusion. The explanatory exclusion principle hinders the acceptance of two causal explanations for a single effect unless an acceptable relation exists between the two purported causes. In this paper I will concentrate on the epistemological version of the principle, including Kim’s acceptable relations, and contrast it with a survey of Jackson’s and Pettit’s program explanations. My aim is to discover whether program explanations expound an acceptable relation already covered by Kim or present an additional way of understanding how two causal explanations of the same phenomenon can be accepted. Jackson and Pettit say: “The notion of a programming property does not just explain how an inefficacious property can be relevant to the causation of an event. It also shows how a program explanation can have a significance that remains in the presence of an explanation invoking the corresponding I

The expressiveness of spider diagrams augmented with constants

Spider diagrams are a visual language for expressing logical statements or constraints. Several sound and complete spider diagram systems have been developed and it has been shown that they are equivalent in expressive power to monadic first order logic with equality. However, these sound and complete spider diagram systems do not contain syntactic elements analogous to constants in first order predicate logic. We extend the spider diagram language to include constant spiders which represent specific individuals. Formal semantics are given for the extended diagram language. We prove that this extended system is equivalent in expressive power to the language of spider diagrams without constants and, hence, equivalent to monadic first order logic with equality.

Well-founded and stable semantics of logic programs with aggregates

AbstractIn this paper, we present a framework for the semantics and the computation of aggregates in the context of logic programming. In our study, an aggregate can be an arbitrary interpreted second order predicate or function. We define extensions of the Kripke-Kleene, the well-founded and the stable semantics for aggregate programs. The semantics is based on the concept of a three-valuedimmediate consequence operatorof an aggregate program. Such an operatorapproximatesthe standard two-valued immediate consequence operator of the program, and induces a unique Kripke-Kleene model, a unique well-founded model and a collection of stable models. We study different ways of defining such operators and thus obtain a framework of semantics, offering different trade-offs betweenprecisionandtractability. In particular, we investigate conditions on the operator that guarantee that the computation of the three types of semantics remains on the same level as for logic programs without aggregates. Other results show that, in practice, even efficient three-valued immediate consequence operators which are very low in the precision hierarchy, still provide optimal precision.

Story (first order predicate) logic

This article is an attempt to clarify the idea that narratives cohere by representing stories. Stories are causally related in the way proposed by Noël Carroll, i.e., the events and states constitute necessary conditions or sufficient conditions or INUS-conditions of each other. Then, a general concept of propositional coherence is suggested. It is based on Nelson Goodman's and Joseph Ullian's ideas about unitary formulas. Narrative coherence is defined as the propositional understanding of a text (in the wide sense, including non-verbal narratives) that constitutes one unitary string built upon conditional relations, i.e., relations between individuals matching Carroll's types of conditions.

JTL

We present an overview of JTL (the Java Tools Language, pronounced "Gee-tel"), a novel language for querying JAVA [8] programs. JTL was designed to serve the development of source code software tools for JAVA, and as a small language which to aid programming language extensions to JAVA. Applications include definition of pointcuts for aspect-oriented programming, fixing type constraints for generic programming, specification of encapsulation policies, definition of micro-patterns, etc. We argue that the JTL expression of each of these is systematic, concise, intuitive and general.JTL relies on a simply-typed relational database for program representation, rather than an abstract syntax tree. The underlying semantics of the language is restricted to queries formulated in First Order Predicate Logic augmented with transitive closure (FOPL).Special effort was taken to ensure terse, yet readable expression of logical conditions. The JTL pattern <B>public abstract class</B>, for example, matches all abstract classes which are publicly accessible, while <B>class</B> (<B>public</B> clone();) matches all classes in which method clone is public. To this end, JTL relies on a DATALOG-like syntax and semantics, enriched with quantifiers and pattern matching which all but entirely eliminate the need for recursive calls.JTL's query analyzer gives special attention to the fragility of the "closed world assumption" in examining JAVA software, and determines whether a query relies on such an assumption.The performance of the JTL interpreter is comparable to that of JQuery after it generated its database cache, and at least an order of magnitude faster when the cache has to be rebuilt.

A contextualist treatment of the predicate of existence

I first give a very short characterization of contextualism in the philosophy of language; then I present the traditional debate about the question whether “exists” is a first or second order predicate, to conclude, firstly, that there is a first order as well as a second order use for that predicate, with no ambiguity, and, secondly, that the debate was couched in too restrictive terms. I defend that there is a huge variety of contexts to be scrutinized, and that a contextualist approach could be useful in that discussion. I close the paper with a critical note to what I call “serious ontology”. Key words: existence as a predicate, contextualism, ontology, philosophy of language.

Reasoning About Partial Functions in the Formal Development of Programs

Partial functions and operators are used extensively in the formal development of programs and thus development methods have to clarify how to reason about them. There are a number of approaches which cover up the fact that “First Order Predicate Calculus” does not handle undefined logical values. There is also at least one specific “Logic of Partial Functions” (LPF) which tackles the issue at its root by using a weaker logic. Recently, we have come to realise that LPF fits a particular way of developing programs. This paper explains why LPF is a suitable logic for “posit and prove” development and explores some problems that other approaches present.

Formal Ontology and Extensions of Order-Sorted Logic

This paper presents several extensions of order-sorted logic based on the notion of property classification in formal ontology. The refined order-sorted language contains types (as rigid sorts), anti-rigid sorts, and unary predicates in order to distinctly express the following properties: substantial sorts, non-substantial sorts, and non-sortal properties. For many separated knowledge bases constructed using the logic, we propose an enriched reasoning mechanism such that each independent knowledge base can extract rigid property information from other knowledge bases (called rigid property derivation). Additionally, we classify (i) anti-rigid properties on the basis of their dependences on time, situation, and belief and (ii) non-sortal properties on the basis of the countability of the elements of the properties.

En torno a los predicativos descriptivos del sujeto y los "estados" "de estadio" como predicados primarios

This article deals with the hypothesis that stative predicates do not occur with subject-oriented adjunct secondary predicates. I argue that the concept of 'slate' is too broad, that we must consider the aspectual diversity of 'states' and the lexical properties of predicates in order to explain constructions with secondary predicates. With this aim, I have revised the most common subdivisions of 'slates' and the sometimes elusive boundaries between 'sates' and 'activities', and I have also examined some sentences with subject-oriented secondary predicates and 'stage-level' 'states' as primary predicates.

First-order expressibility of languages with neutral letters or: The Crane Beach conjecture

A language L over an alphabet A is said to have a neutral letter if there is a letter e ∈ A such that inserting or deleting e's from any word in A * does not change its membership or non-membership in L. The presence of a neutral letter affects the definability of a language in first-order logic. It was conjectured that it renders all numerical predicates apart from the order predicate useless, i.e., that if a language L with a neutral letter is not definable in first-order logic with linear order, then it is not definable in first-order logic with any set N of numerical predicates. Named after the location of its first, flawed, proof this conjecture is called the Crane Beach conjecture (CBC, for short). The CBC is closely related to uniformity conditions in circuit complexity theory and to collapse results in database theory. We investigate the CBC in detail, showing that it fails for N = { + , × } , or, possibly stronger, for any set N that allows counting up to the m times iterated logarithm, for any constant m. On the positive side, we prove the conjecture for the case of all monadic numerical predicates, for the addition predicate + , for the fragment BC ( Σ 1 ) of first-order logic, for regular languages, and for languages over a binary alphabet. We explain the precise relation between the CBC and so-called natural-generic collapse results in database theory. Furthermore, we introduce a framework that gives better understanding of what exactly may cause a failure of the conjecture.

Domain Restriction and the Arguments of Quantificational Determiners

No abstract.

Comparison of first order predicate logic, fuzzy logic and non-monotonic logic as knowledge representation methodology

Abstract The aim of this paper is to compare first order predicate logic, fuzzy logic and non-monotonic logic as knowledge representation methods. First, we define five properties of knowledge; conceptualization, transfer, modification, integration and decomposition. We also evaluate first order predicate logic, fuzzy logic and non-monotonic logic for the above properties, in the view of accuracy, complexity, and completeness. We then prove that the complexities of the three methods are NP-complete. We use this information to design a heuristic algorithm tested on probabilistic input to evaluate accuracy and completeness. With the results, we compare weaknesses and strengths of each method.

An approach to infinitary temporal proof theory

Aim of this work is to investigate from a proof-theoretic viewpoint a propositional and a predicate sequent calculus with an ω–type schema of inference that naturally interpret the propositional and the predicate until–free fragments of Linear Time Logic LTL respectively. The two calculi are based on a natural extension of ordinary sequents and of standard modal rules. We examine the pure propositional case (no extralogical axioms), the propositional and the first order predicate cases (both with a possibly infinite set of extralogical axioms). For each system we provide a syntactic proof of cut elimination and a proof of completeness.