相关论文: On the size of disjunctive formulas in the $\mu$-c…
Guarded normal form requires occurrences of fixpoint variables in a {\mu}-calculus-formula to occur under the scope of a modal operator. The literature contains guarded transformations that effectively bring a {\mu}-calculus-formula into…
We present the concept of a disjunctive basis as a generic framework for normal forms in modal logic based on coalgebra. Disjunctive bases were defined in previous work on completeness for modal fixpoint logics, where they played a central…
We introduce a new notion of structural refinement, a sound abstraction of logical implication, for the modal nu-calculus. Using new translations between the modal nu-calculus and disjunctive modal transition systems, we show that these two…
In the modal mu-calculus, a formula is well-formed if each recursive variable occurs underneath an even number of negations. By means of De Morgan's laws, it is easy to transform any well-formed formula into an equivalent formula without…
We discuss and compare complexity measures for the modal $\mu$-calculus, focusing on size and alternation depth. As a yardstick we take Wilke's alternating tree automata, which we shall call parity formulas in the text. Building on work by…
Generalizing standard monadic second-order logic for Kripke models, we introduce monadic second-order logic interpreted over coalgebras for an arbitrary set functor. We then consider invariance under behavioral equivalence of MSO-formulas.…
This paper studies the relationship between disjunctive form, a syntactic normal form for the modal mu calculus, and the alternation hierarchy. First it shows that all disjunctive formulas which have equivalent tableau have the same…
The modal mu-calculus is obtained by adding least and greatest fixed-point operators to modal logic. Its alternation hierarchy classifies the mu-formulas by their alternation depth: a measure of the codependence of their least and greatest…
The topological $\mu$-calculus has gathered attention in recent years as a powerful framework for representation of spatial knowledge. In particular, spatial relations can be represented over finite structures in the guise of weakly…
In this paper, we present a general realizability semantics for the simply typed $\lambda\mu$-calculus. Then, based on this semantics, we derive both weak and strong normalization results for two versions of the $\lambda\mu$-calculus…
We study the topological $\mu$-calculus, based on both Cantor derivative and closure modalities, proving completeness, decidability and FMP over general topological spaces, as well as over $T_0$ and $T_D$ spaces. We also investigate…
The paper explores properties of the {\L}ukasiewicz {\mu}-calculus, or {\L}{\mu} for short, an extension of {\L}ukasiewicz logic with scalar multiplication and least and greatest fixed-point operators (for monotone formulas). We observe…
We explore the theory of illfounded and cyclic proofs for the propositional modal $\mu$-calculus. A fine analysis of provability for classical and intuitionistic modal logic provides a novel bridge between finitary, cyclic and illfounded…
We present a syntactic cut-elimination procedure for the alternation-free fragment of the modal mu-calculus. Cut reduction is carried out within a cyclic proof system, where proofs are finitely branching but may be non-wellfounded. The…
The paper explores properties of {\L}ukasiewicz mu-calculus, a version of the quantitative/probabilistic modal mu-calculus containing both weak and strong conjunctions and disjunctions from {\L}ukasiewicz (fuzzy) logic. We show that this…
Generalizing standard monadic second-order logic for Kripke models, we introduce monadic second-order logic interpreted over coalgebras for an arbitrary set functor. Similar to well-known results for monadic second-order logic over trees,…
Inspired by a recent graphical formalism for lambda-calculus based on linear logic technology, we introduce an untyped structural lambda-calculus, called lambda j, which combines actions at a distance with exponential rules decomposing the…
A landmark result in the study of logics for formal verification is Janin & Walukiewicz's theorem, stating that the modal $\mu$-calculus ($\mu\mathrm{ML}$) is equivalent modulo bisimilarity to standard monadic second-order logic (here…
We prove a general decomposition theorem for the modal $\mu$-calculus $L_\mu$ in the spirit of Feferman and Vaught's theorem for disjoint unions. In particular, we show that if a structure (i.e., transition system) is composed of two…
In this note, we determine, by a disjunctive normal form theorem, which functions on the standard $n$-nuanced \L ukasiewicz-Moisil algebra are representable by formulas and we show how this result may help in establishing the structure of…