Explicit mathematics and operational set theory: some ontological comparisons

We discuss several ontological properties of explicit mathematics and operational set theory: global choice, decidable classes, totality and extensionality of operations, function spaces, class and set formation via formulas that contain the definedness predicate and applications.

A new model construction by making a detour via intuitionistic theories II: Interpretability lower bound of Feferman's explicit mathematics T0

We partially solve a long-standing problem in the proof theory of explicit mathematics or the proof theory in general. Namely, we give a lower bound of Feferman’s system T0 of explicit mathematics (but only when formulated on classical logic) with a concrete interpretat ion of the subsystem Σ12-AC+ (BI) of second order arithmetic inside T0. Whereas a lower bound proof in the sense of proof-theoretic reducibility or of ordinalanalysis was already given in 80s, the lower bound in the sense of interpretability we give here is new. We apply the new interpretation method developed by the author and Zumbrunnen (2015), which can be seen as the third kind of model construction method for classical theories, after Cohen’s forcing and Krivine’s classical realizability. It gives us an interpretation between classical theories, by composing interpretations between intuitionistic theories.

Offline grammar-based recognition of handwritten sentences

This paper proposes a sequential coupling of a Hidden Markov Model (HMM) recognizer for offline handwritten English sentences with a probabilistic bottom-up chart parser using Stochastic Context-Free Grammars (SCFG) extracted from a text corpus. Based on extensive experiments, we conclude that syntax analysis helps to improve recognition rates significantly.

Capturing How Objects Flow At Runtime

Most of today's dynamic analysis approaches are based on method traces. However, in the case of object-orientation understanding program execution by analyzing method traces is complicated because the behavior of a program depends on the sharing and the transfer of object references (aliasing). We argue that trace-based dynamic analysis is at a too low level of abstraction for object-oriented systems. We propose a new approach that captures the life cycle of objects by explicitly taking into account object aliasing and how aliases propagate during the execution of the program. In this paper, we present in detail our new meta-model and discuss future tracks opened by it.