Searcharxiv⌕ Search

arXiv subjects

Răzvan Diaconescu

Publications and source records attributed to Răzvan Diaconescu.

8 recordsLinked to original sources
arXiv2025

Computational Modelling for Combinatorial Game Strategies

We develop a generic computational model that can be used effectively for establishing the existence of winning strategies for concrete finite combinatorial games. Our modelling is (equational) logic-based involving advanced techniques from algebraic specification, and it can be executed by equational programming systems such as those from the OBJ-family. We show how this provides a form of experimental mathematics for strategy problems involving combinatorial games. We do this by defining general methods and by illustrating these with case studies.

cs.LO↗
arXiv2025

In between myth and reality: AI for math -- a case study in category theory

Recently, there is an increasing interest in understanding the performance of AI systems in solving math problems. A multitude of tests have been performed, with mixed conclusions. In this paper we discuss an experiment we have made in the direction of mathematical research, with two of the most prominent contemporary AI systems. One of the objective of this experiment is to get an understanding of how AI systems can assist mathematical research. Another objective is to support the AI systems developers by formulating suggestions for directions of improvement.

cs.AI↗
arXiv2022

Non-determinsitic algebraic rewriting as adjunction

We develop a general model theoretic semantics to rewriting beyond the usual confluence and termination assumptions. This is based on preordered algebra which is a model theory that extends many sorted algebra. In this framework we characterise rewriting in arbitrary algebras rather than term algebras (called algebraic rewriting) as a persistent adjunction and use this result, on the one hand for proving the soundness and the completeness of an abstract computational model of rewriting that underlies the non-deterministic programming with Maude and CafeOBJ, and on the other hand for developing a compositionality result for algebraic rewriting in the context of the pushout-based modularisation technique.

math.LO↗
arXiv2021

Decompositions of Stratified Institutions

The theory of stratified institutions is a general axiomatic approach to model theories where the satisfaction is parameterised by states of the models. In this paper we further develop this theory by introducing a new technique for representing stratified institutions which is based on projecting to such simpler structures. On the one hand this can be used for developing general results applicable to a wide variety of already existing model theories with states, such as those based on some form of Kripke semantics. On the other hand this may serve as a template for defining new such model theories. In this paper we emphasise on the former application of this technique by developing general results on model amalgamation and on existence diagrams for stratified institutions. These are two most useful properties to have in institution theoretic model theory.

math.LO↗
arXiv2017

Generic partiality for $\frac{3}{2}$-institutions

$\frac{3}{2}$-institutions have been introduced as an extension of institution theory that accommodates implicitly partiality of the signature morphisms together with its syntactic and semantic effects. In this paper we show that ordinary institutions that are equipped with an inclusion system for their categories of signatures generate naturally $\frac{3}{2}$ -institutions with explicit partiality for their signature morphisms. This provides a general uniform way to build 3 -institutions for the foundations of conceptual blending and software evolution. Moreover our general construction allows for an uniform derivation of some useful technical properties.

math.LO↗
arXiv2017

3/2-Institutions: an institution theory for conceptual blending

We develop an extension of institution theory that accommodates implicitly the partiality of the signature morphisms and its syntactic and semantic effects. This is driven primarily by applications to conceptual blending, but other application domains are possible (such as software evolution). The particularity of this extension is a reliance on ordered-enriched categorical structures.

math.LO↗
arXiv2016

Implicit Kripke Semantics and Ultraproducts in Stratified Institutions

We propose stratified institutions (a decade old generalised version of the theory of institutions of Goguen and Burstall) as a fully abstract model theoretic approach to modal logic. This allows for a uniform treatment of model theoretic aspects across the great multiplicity of contemporary modal logic systems. Moreover Kripke semantics (in all its manifold variations) is captured in an implicit manner free from the sometimes bulky aspects of explicit Kripke structures, also accommodating other forms of concrete semantics for modal logic systems. The conceptual power of stratified institutions is illustrated with the development of a modal ultraproducts method that is independent of the concrete details of the actual modal logical systems. Consequently, a wide array of compactness results in concrete modal logics may be derived easily.

math.LO↗