Complete Additivity and Modal Incompleteness

In this paper, we tell a story about incompleteness in modal logic. The story weaves together a paper of van Benthem, `Syntactic aspects of modal incompleteness theorems,' and a longstanding open question: whether every normal modal logic can be characterized by a class of completely additive modal algebras, or as we call them, V-BAOs. Using a first-order reformulation of the property of complete additivity, we prove that the modal logic that starred in van Benthem's paper resolves the open question in the negative. In addition, for the case of bimodal logic, we show that there is a naturally occurring logic that is incomplete with respect to V-BAOs, namely the provability logic GLB. We also show that even logics that are unsound with respect to such algebras do not have to be more complex than the classical propositional calculus. On the other hand, we observe that it is undecidable whether a syntactically defined logic is V-complete. After these results, we generalize the Blok Dichotomy to degrees of V-incompleteness. In the end, we return to van Benthem's theme of syntactic aspects of modal incompleteness

Current research on G\"odel's incompleteness theorems

We give a survey of current research on G\"{o}del's incompleteness theorems from the following three aspects: classifications of different proofs of G\"{o}del's incompleteness theorems, the limit of the applicability of G\"{o}del's first incompleteness theorem, and the limit of the applicability of G\"{o}del's second incompleteness theorem.Comment: 54 pages, final accepted version, to appear in The Bulletin of Symbolic Logi

AN INSTITUTIONAL ECONOMIC APPRAISAL OF WORKER EQUITY SCHEMES IN AGRICULTURE:

The institutional economic appraisal conducted in this paper confirms that equity schemes are subject to institutional incompleteness as proposed in ICT. The incompleteness stem from the lack of verifiability related to social capital, embeddedness, governance and micro performance. In addition, they lack the requisite ex ante incentives to enable ex post adaptation, counterveilance over opportunism, and the distribution of residual claims and control. The first reason for incompleteness emanate from the motivations of the initiators, which is opportunism by landowners to secure their assets in the face of uncertainty and/or enhance their returns in the marketplace. The lack of worker effort and options in the early stages raises credible commitment questions. Examining the governance aspects of equity schemes reveal that they are consistent with modern trends to separate ownership and control. However, a key concern is the asymmetry in human capital and subsequently in power, residual control, gratification, and ultimately economic empowerment. The analysis is aimed at identifying the incentives and innovations required to make equity schemes, as a type of shareholder contract, more complete and credible in an empowerment context. Recommendations towards institutional innovation are offered.Labor and Human Capital,

Initial Draft of a Possible Declarative Semantics for the Language

This article introduces a preliminary declarative semantics for a subset of the language Xcerpt (so-called grouping-stratifiable programs) in form of a classical (Tarski style) model theory, adapted to the specific requirements of Xcerpt’s constructs (e.g. the various aspects of incompleteness in query terms, grouping constructs in rule heads, etc.). Most importantly, the model theory uses term simulation as a replacement for term equality to handle incomplete term specifications, and an extended notion of substitutions in order to properly convey the semantics of grouping constructs. Based upon this model theory, a fixpoint semantics is also described, leading to a first notion of forward chaining evaluation of Xcerpt program

Interpreting Embedding Models of Knowledge Bases: A Pedagogical Approach

Knowledge bases are employed in a variety of applications from natural language processing to semantic web search; alas, in practice their usefulness is hurt by their incompleteness. Embedding models attain state-of-the-art accuracy in knowledge base completion, but their predictions are notoriously hard to interpret. In this paper, we adapt "pedagogical approaches" (from the literature on neural networks) so as to interpret embedding models by extracting weighted Horn rules from them. We show how pedagogical approaches have to be adapted to take upon the large-scale relational aspects of knowledge bases and show experimentally their strengths and weaknesses.Comment: presented at 2018 ICML Workshop on Human Interpretability in Machine Learning (WHI 2018), Stockholm, Swede

Microprogramming and microprocessors in the Netherlands

This paper gives a short survey of the activities in the field of microprocessors and microprogramming in the Netherlands. In the first part of it the activies within the Universities and non commercial institutes are mentioned. The second part deals with the industrial activity. The author is aware of the incompleteness of the survey. The reason for it is twofold. First; Some of the activies, especially in the industrie, have confidential aspects. The information may not yet appear in a paper like this. Second; He is not aware of all activities carried out in the field. A list of names of the institutes etcand eventual contactpersons is included. A literature list is not added, because not much literature is available now

On the Inherent Incompleteness of Scientific Theories

We examine the question of whether scientific theories can ever be complete. For two closely related reasons, we will argue that they cannot. The first reason is the inability to determine what are “valid empirical observations”, a result that is based on a self-reference Gödel/Tarski-like proof. The second reason is the existence of “meta-empirical” evidence of the inherent incompleteness of observations. These reasons, along with theoretical incompleteness, are intimately connected to the notion of belief and to theses within the philosophy of science: the Quine-Duhem (and underdetermination) thesis and the observational/theoretical distinction failure. Some puzzling aspects of the philosophical theses will become clearer in light of these connections. Other results that follow are: no absolute measure of the informational content of empirical data, no absolute measure of the entropy of physical systems, and no complete computer simulation of the natural world are possible. The connections with the mathematical theorems of Gödel and Tarski reveal the existence of other connections between scientific and mathematical incompleteness: computational irreducibility, complexity, infinity, arbitrariness and self-reference. Finally, suggestions will be offered of where a more rigorous (or formal) “proof” of scientific incompleteness can be found

The Ontic Probability Interpretation of Quantum Theory - Part I: The Meaning of Einstein's Incompleteness Claim

Ignited by Einstein and Bohr a century ago, the philosophical struggle about Reality is yet unfinished, with no signs of a swift resolution. Despite vast technological progress fueled by the iconic EPR paper (EPR), the intricate link between ontic and epistemic aspects of Quantum Theory (QT) has greatly hindered our grip on Reality and further progress in physical theory. Fallacies concealed by tortuous logical negations made EPR comprehension much harder than it could have been had Einstein written it himself in German. It is plagued with preconceptions about what a physical property is, the 'Uncertainty Principle', and the Principle of Locality. Numerous interpretations of QT vis à vis Reality exist and are keenly disputed. This is the first of a series of articles arguing for a physical interpretation called ‘The Ontic Probability Interpretation’ (TOPI). A gradual explanation of TOPI is given intertwined with a meticulous logico-philosophical scrutiny of EPR. Part I focuses on the meaning of Einstein’s ‘Incompleteness’ claim. A conceptual confusion, a preconception about Reality, and a flawed dichotomy are shown to be severe obstacles for the EPR argument to succeed. Part II analyzes Einstein’s ‘Incompleteness/Nonlocality Dilemma’. Future articles will further explain TOPI, demonstrating its soundness and potential for nurturing theoretical progress

Completing Queries: Rewriting of IncompleteWeb Queries under Schema Constraints

Reactive Web systems, Web services, and Web-based publish/ subscribe systems communicate events as XML messages, and in many cases require composite event detection: it is not sufficient to react to single event messages, but events have to be considered in relation to other events that are received over time. Emphasizing language design and formal semantics, we describe the rule-based query language XChangeEQ for detecting composite events. XChangeEQ is designed to completely cover and integrate the four complementary querying dimensions: event data, event composition, temporal relationships, and event accumulation. Semantics are provided as model and fixpoint theories; while this is an established approach for rule languages, it has not been applied for event queries before