Related papers: Complete Quantum Relational Hoare Logics from Opti…
We develop the first two heap logics that have implicit heaplets and that admit FO-complete program verification. The notion of FO-completeness is a theoretical guarantee that all theorems that are valid when recursive definitions are…
The failure of distributivity in quantum logic is motivated by the principle of quantum superposition. However, this principle can be encoded differently, i.e., in different logico-algebraic objects. As a result, the logic of experimental…
We reconstruct finite-dimensional quantum theory with superselection rules, which can describe hybrid quantum-classical systems, from four purely operational postulates: symmetric sharpness, complete mixing, filtering, and local equality.…
In the tradition of toy models of quantum mechanics in vector spaces over finite fields (e.g., Schumacher and Westmoreland's "modal quantum theory"), one finite field stands out, 2, since vectors over 2 have an interpretation as natural…
We show the functional completeness for the connectives of the non-trivial negation inconsistent logic C by using a well-established method implementing purely proof-theoretic notions only. Firstly, given that C contains a strong negation,…
The emphasis is made on the juxtaposition of (quantum~theorem) proving versus quantum (theorem~proving). The logical contents of verification of the statements concerning quantum systems is outlined. The Zittereingang (trembling input)…
We formalize the correspondence between quantum states and quantum operations isometrically, and harness its consequences. This correspondence was already implicit in the various proofs of the operator sum representation of Completely…
We combine the concepts of modal logics and many-valued logics in a general and comprehensive way. Namely, given any finite linearly ordered set of truth values and any set of propositional connectives defined by truth tables, we define the…
Quantum transport plays a central role in both fundamental physics and the development of quantum technologies. While significant progress has been made in understanding transport phenomena in quantum systems, methods for optimizing…
In previous works, a tableau calculus has been defined, which constitutes a decision procedure for hybrid logic with the converse and global modalities and a restricted use of the binder. This work shows how to extend such a calculus to…
We explore a connection between quantum logic and quantum computing.
Fiore and Hur recently introduced a conservative extension of universal algebra and equational logic from first to second order. Second-order universal algebra and second-order equational logic respectively provide a model theory and a…
This paper provides the quantum treatment of the relational quadrilateral. The underlying reduced configuration spaces are $\mathbb{CP}^2$ and the cone over this, C($\mathbb{CP}^2$). We consider exact free and isotropic HO potential cases…
We define and study logics in the framework of probabilistic team semantics and over metafinite structures. Our work is paralleled by the recent development of novel axiomatizable and tractable logics in team semantics that are closed under…
We introduce an operational rewriting-based semantics for strictly positive nested higher-order (co)inductive types. The semantics takes into account the "limits" of infinite reduction sequences. This may be seen as a refinement and…
The development of the new logic of partitions (= equivalence relations) dual to the usual Boolean logic of subsets, and its quantitative version as the new logical theory of information provide the basic mathematical concepts to describe…
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…
In the regime of bounded transportation costs, additive approximations for the optimal transport problem are reduced (rather simply) to relative approximations for positive linear programs, resulting in faster additive approximation…
Quantified Boolean logic results from adding operators to Boolean logic for existentially and universally quantifying variables. This extends the reach of Boolean logic by enabling a variety of applications that have been explored over the…
We explore a kind of first-order predicate logic with intended semantics in the reals. Compared to other approaches in the literature, we work predominantly in the multiplicative reals $[0,\infty]$, showing they support three generations of…