Related papers: Quantifiers metamorphoses. Generalizations, variat…
The number of quantifiers needed to express first-order (FO) properties is captured by two-player combinatorial games called multi-structural games. We analyze these games on binary strings with an ordering relation, using a technique we…
We propose a system for the interpretation of anaphoric relationships between unbound pronouns and quantifiers. The main technical contribution of our proposal consists in combining generalized quantifiers with dependent types. Empirically,…
Realism -- the idea that the concepts in physical theories refer to 'things' existing in the real world -- is introduced as a tool to analyze the status of the wave-function. Although the physical entities are recognized by the existence of…
This note presents a simple and unified formulation of the most fundamental structures used in quantum information with qubits, arbitrary dimension qudits, and quantum continuous variables. This \emph{general quantum variables} construction…
It is the goal of this article to extend the notion of quantization from the standard interpretation focused on non-commuting observables defined starting from classical analogues, to the topological equivalents defined in terms of…
We propose a formalization of generic algorithms that includes analog algorithms. This is achieved by reformulating and extending the framework of abstract state machines to include continuous-time models of computation. We prove that every…
Computability logic is a formal theory of computational tasks and resources. Formulas in it represent interactive computational problems, and "truth" is understood as algorithmic solvability. Interactive computational problems, in turn, are…
This paper is a reflexion on the computability of natural language semantics. It does not contain a new model or new results in the formal semantics of natural language: it is rather a computational analysis of the logical models and…
In a recent work, arXiv:2503.05884, we proposed a unified notion of nonclassicality that applies to arbitrary processes in quantum theory, including individual quantum states, measurements, channels, set of these, etc. This notion is…
The world of mathematics is often considered abstract, with its symbols, concepts, and topics appearing unrelated to physical objects. However, it is important to recognize that the development of mathematics is fundamentally influenced by…
Many physicists limit oneself to an instrumentalist description of quantum phenomena and ignore the problems of foundation and interpretation of quantum mechanics. This instrumentalist approach results to "specialization barbarism" and mass…
Every quantum physical system can be considered the ''shadow'' of a special kind of classical system. The system proposed here is classical mainly because each observable function has a well precise value on each state of the system: an…
Quotients and comprehension are fundamental mathematical constructions that can be described via adjunctions in categorical logic. This paper reveals that quotients and comprehension are related to measurement, not only in quantum logic,…
The indeterministic outcome of a measurement of an individual quantum is certified by the impossibility of the simultaneous, definite, deterministic pre-existence of all conceivable observables from physical conditions of that quantum…
Formal definitions of quantities, quantity spaces, dimensions and dimension groups are introduced. Based on these concepts, a theoretical framework and a practical algorithm for dimensional analysis are developed, and examples of…
This paper addresses the problem of checking invariant properties for a large class of symbolic transition systems, defined by a combination of SMT theories and quantifiers. State variables can be functions from an uninterpreted sort…
Quantified Boolean formulas (QBFs) generalize propositional formulas by admitting quantifications over propositional variables. QBFs can be viewed as (restricted) formulas of first-order predicate logic and easy translations of QBFs into…
In previous work with J. Hedges, we formalised a generalised quantifiers theory of natural language in categorical compositional distributional semantics with the help of bialgebras. In this paper, we show how quantifier scope ambiguity can…
We introduce notions of simulation between semiring-weighted automata as models of quantitative systems. Our simulations are instances of the categorical/coalgebraic notions previously studied by Hasuo---hence soundness against language…
The debate instigated by the seminal works of Einstein, Podolsky, Rosen, and Bell, put the notions of realism and nonlocality at the core of almost all philosophical and physical discussions underlying the foundations of quantum mechanics.…