Related papers: Recovering Quantum Logic within an Extended Classi…
We analyze the logical foundations of quantum mechanics (QM) by stressing non-objectivity of quantum observables which is a consequence of the absence of logical atoms in QM. We argue that the matter of quantum non-objectivity is that, on…
The quantum measurement problem is often presented as a conflict between unitary evolution and non-unitary collapse. Drawing on Wittgenstein's later philosophy of language and Bohr's principle of complementarity, we argue that this conflict…
In this paper, we discuss content and context for quantum properties. We give some examples of why quantum properties are problematic: they depend on the context in a non-trivial way. We then connect this difficulty with properties to the…
The language of epistemic specifications and epistemic logic programs extends disjunctive logic programs under the stable model semantics with modal constructs called subjective literals. Using subjective literals, it is possible to check…
A classical logic exhibits a threefold inner structure comprising an algebra of propositions `A', a space of ``truth values'' `V', and a distinguished family of mappings `phi' from propositions to truth values. Classically A is a Boolean…
Quantum field theory currently has a single standard mathematical characterization (the Standard Model), but no single accepted conceptual framework to interpret the mathematics. Many of these conceptualizations rely on intuitive concepts…
Quantified CTL (QCTL) is a well-studied temporal logic that extends CTL with quantification over atomic propositions. It has recently come to the fore as a powerful intermediary framework to study logics for strategic reasoning. We extend…
I summarize a research program that aims to reconstruct quantum theory from a fundamental physical principle that, while a quantum system has no intrinsic hidden variables, it can be understood using a reference measurement. This program…
Deep and shallow embeddings of non-classical logics in classical higher-order logic have been explored, implemented, and used in various reasoning tools in recent years. This paper presents a method for the simultaneous deployment of deep…
Real-world arguments in text and dialogues are normally enthymemes (i.e. some of their premises and/or claims are implicit). Natural language processing (NLP) methods for handling enthymemes can potentially identify enthymemes in text but…
Semantic degeneracy represents a fundamental property of natural language that extends beyond simple polysemy to encompass the combinatorial explosion of potential interpretations that emerges as semantic expressions increase in complexity.…
Over the past few decades, non-monotonic reasoning has developed to be one of the most important topics in computational logic and artificial intelligence. Different ways to introduce non-monotonic aspects to classical logic have been…
Large language models (LLMs) are a promising venue for natural language understanding and generation tasks. However, current LLMs are far from reliable: they are prone to generate non-factual information and, more crucially, to contradict…
This paper deals with the foundations of quantum mechanics. We start by outlining the characterisation, due to Birkhoff and Von Neumann, of the logical structures of the theories of classical physics and quantum mechanics, as boolean and…
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…
Conventional canonical quantization procedures directly link various c-number and q-number quantities. Here, we advocate a different association of classical and quantum quantities that renders classical theory a natural subset of quantum…
Recently, arXiv:2312.16035 showed that all logics based on Boolean Normal monotonic three-valued schemes coincide with classical logic when defined using a strict-tolerant standard ($\mathbf{st}$). Conversely, they proved that under a…
Theories of natural language and concepts have been unable to model the flexibility, creativity, context-dependence, and emergence, exhibited by words, concepts and their combinations. The mathematical formalism of quantum theory has…
We introduce Qunity, a new quantum programming language designed to treat quantum computing as a natural generalization of classical computing. Qunity presents a unified syntax where familiar programming constructs can have both quantum and…
We present a novel linear $\lambda$-calculus for Classical Multiplicative Exponential Linear Logic (\MELL) along the lines of the propositions-as-types paradigm. Starting from the standard term assignment for Intuitionistic Multiplicative…