Related papers: Satisfiability of CTL* with constraints
Quantified modal logic provides a natural logical language for reasoning about modal attitudes even while retaining the richness of quantification for referring to predicates over domains. But then most fragments of the logic are…
This unpublished note is an alternate, shorter (and hopefully more readable) proof of the decidability of all minimal models. The decidability follows from a proof of the existence of a cellular term in each observational equivalence class…
Hyperproperties, which generalize trace properties by relating multiple traces, are widely studied in information-flow security. Recently, a number of logics for hyperproperties have been proposed, and there is a need to understand their…
Morrill and Valentin in the paper "Computational coverage of TLG: Nonlinearity" considered an extension of the Lambek calculus enriched by a so-called "exponential" modality. This modality behaves in the "relevant" style, that is, it allows…
The Guarded Fragment (GF) is a well-established decidable fragment of first-order logic. We study an extension of GF with nested equivalence relations, namely a family of distinguished binary predicates $E_1, E_2, \dots$ interpreted as…
We stratify intuitionistic first-order logic over $(\forall,\to)$ into fragments determined by the alternation of positive and negative occurrences of quantifiers (Mints hierarchy). We study the decidability and complexity of these…
We prove a relative decidability result for perfectoid fields. This applies to show that the fields $\mathbb{Q}_p(p^{1/p^{\infty}})$ and $\mathbb{Q}_p(\zeta_{p^{\infty}})$ are (existentially) decidable relative to the perfect hull of $…
We study first-order logic over unordered structures whose elements carry a finite number of data values from an infinite domain. Data values can be compared wrt.\ equality. As the satisfiability problem for this logic is undecidable in…
We study the satisfiability and model-checking problems for timed hyperproperties specified with HyperMTL, a timed extension of HyperLTL. Depending on whether interleaving of events in different traces is allowed, two possible semantics can…
Metric Temporal Logic (MTL) and Timed Propositional Temporal Logic (TPTL) are prominent real-time extensions of Linear Temporal Logic (LTL). In general, the satisfiability checking problem for these extensions is undecidable when both the…
The expressive power of interval temporal logics (ITLs) makes them one of the most natural choices in a number of application domains, ranging from the specification and verification of complex reactive systems to automated planning.…
We introduce two variants of computation tree logic CTL based on team semantics: an asynchronous one and a synchronous one. For both variants we investigate the computational complexity of the satisfiability as well as the model checking…
HyperQPTL and HyperQPTL$^+$ are expressive specification languages for hyperproperties, properties that relate multiple executions of a system. Tight complexity bounds are known for HyperQPTL finite-state satisfiability and model-checking.…
We consider the fragment F of first order arithmetic in which quantification is restricted to ''for all but finitely many.'' We show that the integers form an F-elementary substructure of the real numbers. Consequently, the F-theory of…
The standard reasoning problem, concept satisfiability, in the basic description logic ALC is PSPACE-complete, and it is EXPTIME-complete in the presence of unrestricted axioms. Several fragments of ALC, notably logics in the FL, EL, and…
We consider first-order logic over the subword ordering on finite words, where each word is available as a constant. Our first result is that the $\Sigma_1$ theory is undecidable (already over two letters). We investigate the decidability…
We develop a sound, complete and practically implementable tableaux-based decision method for constructive satisfiability testing and model synthesis in the fragment ATL+ of the full Alternating time temporal logic ATL*. The method extends…
We consider the decidability of the verification problem of programs \emph{modulo axioms} --- that is, verifying whether programs satisfy their assertions, when the functions and relations it uses are assumed to interpreted by arbitrary…
We present a classification theorem for a class of unital simple separable amenable ${\cal Z}$-stable $C^*$-algebras by the Elliott invariant. This class of simple $C^*$-algebras exhausts all possible Elliott invariant for unital stably…
We introduce a novel decidable fragment of first-order logic. The fragment is one-dimensional in the sense that quantification is limited to applications of blocks of existential (universal) quantifiers such that at most one variable…