Related papers: Succinctness in subsystems of the spatial mu-calcu…
In this paper, we study computational complexity and expressive power of modal operators for definite descriptions, which correspond to statements `the modal world which satisfies formula \(varphi\)'. We show that adding such operators to…
Is it possible to write significantly smaller formulae when using Boolean operators other than those of the De Morgan basis (and, or, not, and the constants)? For propositional logic, a negative answer was given by Pratt: formulae over one…
We develop a general criterion for cut elimination in sequent calculi for propositional modal logics, which rests on absorption of cut, contraction, weakening and inversion by the purely modal part of the rule system. Our criterion applies…
It is well known that modal satisfiability is PSPACE-complete (Ladner 1977). However, the complexity may decrease if we restrict the set of propositional operators used. Note that there exist an infinite number of propositional operators,…
We study the decidability and expressiveness issues of $\mu$-calculus on data words and data $\omega$-words. It is shown that the full logic as well as the fragment which uses only the least fixpoints are undecidable, while the fragment…
Arithmetic circuits (AC) are circuits over the real numbers with 0/1-valued input variables whose gates compute the sum or the product of their inputs. Positive AC -- that is, AC representing non-negative functions -- subsume many…
We study elementary modal logics, i.e. modal logic considered over first-order definable classes of frames. The classical semantics of modal logic allows infinite structures, but often practical applications require to restrict our…
Introduced by Darwiche (2011), sentential decision diagrams (SDDs) are essentially as tractable as ordered binary decision diagrams (OBDDs), but tend to be more succinct in practice. This makes SDDs a prominent representation language, with…
We propose a $\lambda$-calculus-style formal language, called the $\mu$-syntax, as a lightweight representation of the structure of cyclic operads. We illustrate the rewriting methods behind the formalism by giving a complete step-by-step…
The fully enriched μ-calculus is the extension of the propositional μ-calculus with inverse programs, graded modalities, and nominals. While satisfiability in several expressive fragments of the fully enriched μ-calculus is known…
We investigate the computational complexity of the satisfiability problem of modal inclusion logic. We distinguish two variants of the problem: one for the strict and another one for the lax semantics. Both problems turn out to be…
We generalize the notion of symmetries of propositional formulas in conjunctive normal form to modal formulas. Our framework uses the coinductive models and, hence, the results apply to a wide class of modal logics including, for example,…
It is known that the alternation hierarchy of least and greatest fixpoint operators in the mu-calculus is strict. However, the strictness of the alternation hierarchy does not necessarily carry over when considering restricted classes of…
This paper studies the complexity of classical modal logics and of their extension with fixed-point operators, using translations to transfer results across logics. In particular, we show several complexity results for multi-agent logics…
We introduce the countdown $\mu$-calculus, an extension of the modal $\mu$-calculus with ordinal approximations of fixpoint operators. In addition to properties definable in the classical calculus, it can express (un)boundedness properties…
We study the expressive power and succinctness of order-invariant sentences of first-order (FO) and monadic second-order (MSO) logic on structures of bounded tree-depth. Order- invariance is undecidable in general and, thus, one strives for…
In this paper, we show that theory of processes can be reduced to the theory of spatial logic. Firstly, we propose a spatial logic SL for higher order pi-calculus, and give an inference system of SL. The soundness and incompleteness of SL…
We prove that omega^2 strictly bounds the iterations required for modal definable functions to reach a fixed point across all countable structures. The result corrects and extends the previously claimed result by the first and third authors…
We investigate the expressivity and computational complexity of two modal logics on finite forests equipped with operators to reason on submodels. The logic ML(|) extends the basic modal logic ML with the composition operator | from static…
We compare the expressiveness of two extensions of monadic second-order logic (MSO) over the class of finite structures. The first, counting monadic second-order logic (CMSO), extends MSO with first-order modulo-counting quantifiers,…