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In this thesis we introduce quantum refereed games, which are quantum interactive proof systems with two competing provers. We focus on a restriction of this model that we call "short quantum games" and we prove an upper bound and a lower…
We studied how the local topological structure of sentence-embedding neighborhoods encodes semantic ambiguity. Extending ideas that link word-level polysemy to non-trivial persistent homology, we generalized the concept to full sentences…
A game-theoretic setting provides a mathematical basis for analysis of strategic interaction among competing agents and provides insights into both classical and quantum decision theory and questions of strategic choice. An outstanding…
Justification theory is a unifying semantic framework. While it has its roots in non-monotonic logics, it can be applied to various areas in computer science, especially in explainable reasoning; its most central concept is a justification:…
Bisimilarity as an equivalence notion of systems has been central to process theory. Due to the recent rise of interest in quantitative systems (probabilistic, weighted, hybrid, etc.), bisimilarity has been extended in various ways:…
While Large Language Models have achieved notable success on formal mathematics benchmarks such as MiniF2F, it remains unclear whether these results stem from genuine logical reasoning or semantic pattern matching against pre-training data.…
We present novel semiring semantics for abstract reduction systems (ARSs). More precisely, we provide a weighted version of ARSs, where the reduction steps induce weights from a semiring. Inspired by provenance analysis in database theory…
We provide a logical characterization of non-deterministic polynomial time defined by BSS machines over semirings via existential second-order logic interpreted in the semiring semantics developed by Gr\"adel and Tannen. Furthermore, we…
Game theory provides a mathematical framework for analysing strategic situations involving at least two players. Normal-form games model situations where the players simultaneously pick their moves. In this thesis we explore the strategic…
The sequence form, owing to its compact and holistic strategy representation, has demonstrated significant efficiency in computing normal-form perfect equilibria for two-player extensive-form games with perfect recall. Nevertheless, the…
Research in quantum games has flourished during recent years. However, it seems that opinion remains divided about their true quantum character and content. For example, one argument says that quantum games are nothing but 'disguised'…
We propose a new version of formula size game for modal logic. The game characterizes the equivalence of pointed Kripke-models up to formulas of given numbers of modal operators and binary connectives. Our game is similar to the well-known…
This article presents an overview of computability logic -- the game-semantically constructed logic of interactive computational tasks and resources. There is only one non-overview, technical section in it, devoted to a proof of the…
Game semantics has proven to be a robust method to give compositional semantics for a variety of higher-order programming languages. However, due to the complexity of most game models, game semantics has remained unapproachable for…
Quantum games have proposed a new point of view for the solution of the classical problems and dilemmas in game theory. Certain quantization relationships can be proposed with the objective that a game can be generalized into a quantum…
Many analysis and verifications tasks, such as static program analyses and model-checking for temporal logics reduce to the solution of systems of equations over suitable lattices. Inspired by recent work on lattice-theoretic progress…
Predicate logic is the premier choice for specifying classes of relational structures. Homomorphisms are key to describing correspondences between relational structures. Questions concerning the interdependencies between these two means of…
Formal verification guarantees proof validity but not formalization faithfulness. For natural-language logical reasoning, where models construct axiom systems from scratch without library constraints, this gap between valid proofs and…
Given that theoretical analysis and empirical validation is fundamental to any model, whether conceptual or formal, it is surprising that these two tools of scientific discovery are so often ignored in the contemporary studies of…
We state and prove Kuhn's equivalence theorem for a new representation of games, the intrinsic form. First, we introduce games in intrinsic form where information is represented by $\sigma$-fields over a product set. For this purpose, we…