Towards a unified theory of logic programming semantics: Level mapping characterizations of selector generated models

Currently, the variety of expressive extensions and different semantics created for logic programs with negation is diverse and heterogeneous, and there is a lack of comprehensive comparative studies which map out the multitude of perspectives in a uniform way. Most recently, however, new methodologies have been proposed which allow one to derive uniform characterizations of different declarative semantics for logic programs with negation. In this paper, we study the relationship between two of these approaches, namely the level mapping characterizations due to [Hitzler and Wendt 2005], and the selector generated models due to [Schwarz 2004]. We will show that the latter can be captured by means of the former, thereby supporting the claim that level mappings provide a very flexible framework which is applicable to very diversely defined semantics.Comment: 17 page

Cartesian closed topological and monotopological hulls: A comparison

AbstractThe theory of cartesian closed monotopological hull of a category can be developed in analogy to that of the cartesian closed topological hull. The main objective of this paper is to describe these hulls in terms of one another. On the local level, a comparison between the cartesian objects of a monotopological category and the cartesian objects of its MacNeille completion is carried out. The cartesian closed monotopological hulls of several well-known subcategories of Top are determined

Cartesian closed topological and monotopological hulls: A comparison

AbstractThe theory of cartesian closed monotopological hull of a category can be developed in analogy to that of the cartesian closed topological hull. The main objective of this paper is to describe these hulls in terms of one another. On the local level, a comparison between the cartesian objects of a monotopological category and the cartesian objects of its MacNeille completion is carried out. The cartesian closed monotopological hulls of several well-known subcategories of Top are determined

Pitfalls in machine learning‐based assessment of tumor‐infiltrating lymphocytes in breast cancer: a report of the international immuno‐oncology biomarker working group

The clinical significance of the tumor-immune interaction in breast cancer (BC) has been well established, and tumor-infiltrating lymphocytes (TILs) have emerged as a predictive and prognostic biomarker for patients with triple-negative (estrogen receptor, progesterone receptor, and HER2 negative) breast cancer (TNBC) and HER2-positive breast cancer. How computational assessment of TILs can complement manual TIL-assessment in trial- and daily practices is currently debated and still unclear. Recent efforts to use machine learning (ML) for the automated evaluation of TILs show promising results. We review state-of-the-art approaches and identify pitfalls and challenges by studying the root cause of ML discordances in comparison to manual TILs quantification. We categorize our findings into four main topics; (i) technical slide issues, (ii) ML and image analysis aspects, (iii) data challenges, and (iv) validation issues. The main reason for discordant assessments is the inclusion of false-positive areas or cells identified by performance on certain tissue patterns, or design choices in the computational implementation. To aid the adoption of ML in TILs assessment, we provide an in-depth discussion of ML and image analysis including validation issues that need to be considered before reliable computational reporting of TILs can be incorporated into the trial- and routine clinical management of patients with TNBC

Level Mapping Characterizations of Selector-Generated Models for Logic Programs

Assigning semantics to logic programs via selector generated models (Schwarz 2002/2003) extends several semantics, like the stable, the inflationary, and the stable generated semantics, to programs with arbitrary formulae in rule heads and bodies. We study this approach by means of a unifying framework for characterizing different logic programming semantics using level mappings (Hitzler and Wendt 200x, Hitzler 2003), thereby supporting the claim that this framework is very flexible and applicable to very diversely defined semantics

On hereditary and product-stable quotient maps

summary:It is shown that the quotient maps of a monotopological construct {\bf A} which are preserved by pullbacks along embeddings, projections, or arbitrary morphisms, can be characterized by being quotient maps in appropriate extensions of {\bf A}

Level mapping characterizations of selector generated models for logic programs

Abstract. Assigning semantics to logic programs via selector generated models (Schwarz 2002/2003) extends several semantics, like the stable, the inflationary, and the stable generated semantics, to programs with arbitrary formulae in rule heads and bodies. We study this approach by means of a unifying framework for characterizing different logic programming semantics using level mappings (Hitzler and Wendt 200x, Hitzler 2003), thereby supporting the claim that this framework is very flexible and applicable to very diversely defined semantics.