Related papers: Algebraic semantics for hybrid logics
We investigate atomicity of free algebras and various forms of amalgamation for BL and MV algebras, and also Heyting algebras, though the latter algebras may not be linearly ordered, so strictly speaking their corresponding intuitionistic…
We present our library for Universal Algebra in the UniMath framework dealing with multi-sorted signatures, their algebras, and the basics for equation systems. We show how to implement term algebras over a signature without resorting to…
The stable model semantics had been recently generalized to non-Herbrand structures by several works, which provides a unified framework and solid logical foundations for answer set programming. This paper focuses on the expressiveness of…
Practically and intrinsically, inclusions of operator algebras are of fundamental interest. The subject of this paper is intermediate operator algebras of inclusions. There are two previously known theorems which naturally and completely…
We bring forward a logical system of transition algebras that enhances many-sorted first-order logic using features from dynamic logics. The sentences we consider include compositions, unions, and transitive closures of transition…
The bialgebraic abstract GSOS framework by Turi and Plotkin provides an elegant categorical approach to modelling the operational and denotational semantics of programming and process languages. In abstract GSOS, bisimilarity is always a…
Over a field of characteristic zero we prove two formality conditions. We prove that a dg Lie algebra is formal if and only if its universal enveloping algebra is formal. We also prove that a commutative dg algebra is formal as a dg…
Hybrid programs combine digital control with differential equations, and naturally appear in a wide range of application domains, from biology and control theory to real-time software engineering. The entanglement of discrete and continuous…
We make a start on one of George McNulty's Dozen Easy Problems: "Which finite automatic algebras are dualizable?" We give some necessary and some sufficient conditions for dualizability. For example, we prove that a finite automatic algebra…
Nominal algebra includes $\alpha$-equality and freshness constraints on nominal terms endowed with a nominal set semantics that facilitates reasoning about languages with binders. Nominal unification is decidable and unitary, however, its…
We present a scheme for translating logic programs, which may use aggregation and arithmetic, into algebraic expressions that denote bag relations over ground terms of the Herbrand universe. To evaluate queries against these relations, we…
This paper introduces operators, semantics, characterizations, and solution-independent conditions to guarantee temporal logic specifications for hybrid dynamical systems. Hybrid dynamical systems are given in terms of differential…
Broadly speaking, there are two kinds of semantics-aware assistant systems for mathematics: proof assistants express the semantic in logic and emphasize deduction, and computer algebra systems express the semantics in programming languages…
We consider quantum symmetric algebras, FRT bialgebras and, more generally, intertwining algebras for pairs of Hecke symmetries which represent quantum hom-spaces. The paper makes an attempt to investigate Koszulness and Gorensteinness of…
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…
We study transformational program logics for correctness and incorrectness that we extend to explicitly handle both termination and nontermination. We show that the logics are abstract interpretations of the right image transformer for a…
We provide a sound and complete proof system for an extension of Kleene's ternary logic to predicates. The concept of theory is extended with, for each function symbol, a formula that specifies when the function is defined. The notion of…
Generalized orthomodular posets were introduced recently by D. Fazio, A. Ledda and the first author of the present paper in order to establish a useful tool for studying the logic of quantum mechanics. They investigated structural…
We notice that for any positive integer $k$, the set of $(1,2)$-specialized characters of level $k$ standard $A_{1}^{(1)}$-modules is the same as the set of rescaled graded dimensions of the subspaces of level $2k+1$ standard…
Nominal automata models serve as a formalism for data languages, and in fact often relate closely to classical register models. The paradigm of name allocation in nominal automata helps alleviate the pervasive computational hardness of…