Related papers: On the satisfiability problem for fragments of the…
The first-order theory of addition over the natural numbers, known as Presburger arithmetic, is decidable in double exponential time. Adding an uninterpreted unary predicate to the language leads to an undecidable theory. We sharpen the…
We study several decision problems for counter systems with guards defined by convex polyhedra and updates defined by affine transformations. In general, the reachability problem is undecidable for such systems. Decidability can be achieved…
Strategy Logic (SL, for short) has been introduced by Mogavero, Murano, and Vardi as a useful formalism for reasoning explicitly about strategies, as first-order objects, in multi-agent concurrent games. This logic turns out to be very…
Temporal logics for the specification of information-flow properties are able to express relations between multiple executions of a system. The two most important such logics are HyperLTL and HyperCTL*, which generalise LTL and CTL* by…
Standpoint linear temporal logic SLTL is a recent formalism able to model possibly conflicting commitments made by distinct agents, taking into account aspects of temporal reasoning. In this paper, we analyse the computational properties of…
The interpolant existence problem (IEP) for a logic L is to decide, given formulas P and Q, whether there exists a formula I, built from the shared symbols of P and Q, such that P entails I and I entails Q in L. If L enjoys the Craig…
Separation logic and its variants can describe various properties on pointer programs. However, when it comes to properties on sequences, one may find it hard to formalize. To deal with properties on variable-length sequences and multilevel…
The central open question in Descriptive Complexity is whether there is a logic that characterizes deterministic polynomial time (PTIME) on relational structures. Towards this goal, we define a logic that is obtained from first-order logic…
We address the satisfiability problem for string constraints that combine relational constraints represented by transducers, word equations, and string length constraints. This problem is undecidable in general. Therefore, we propose a new…
In response to a concern raised by Horty, this paper develops a two-tiered, preference-based semantic framework for modeling defeasible conditional obligations. The paper extends a Hansson-Lewis style preference semantics for dyadic deontic…
HyperLTL, the extension of Linear Temporal Logic by trace quantifiers, is a uniform framework for expressing information flow policies by relating multiple traces of a security-critical system. HyperLTL has been successfully applied to…
We solve the satisfiability problem for a three-sorted fragment of set theory (denoted $3LQST_0^R$), which admits a restricted form of quantification over individual and set variables and the finite enumeration operator $\{\text{-},…
The choice of the right trade-off between expressiveness and complexity is the main issue in interval temporal logic. In their seminal paper, Halpern and Shoham showed that the satisfiability problem for HS (the temporal logic of Allen's…
We provide decidability and undecidability results on the model-checking problem for infinite tree structures. These tree structures are built from sequences of elements of infinite relational structures. More precisely, we deal with the…
Model checking linear-time properties expressed in first-order logic has non-elementary complexity, and thus various restricted logical languages are employed. In this paper we consider two such restricted specification logics, linear…
Linear Temporal Logic (LTL) interpreted on finite traces is a robust specification framework popular in formal verification. However, despite the high interest in the logic in recent years, the topic of their quantitative extensions is not…
Maslov's class $\overline{\text{K}}$ is an expressive fragment of First-Order Logic known to have decidable satisfiability problem, whose exact complexity, however, has not been established so far. We show that $\overline{\text{K}}$ has the…
Linear Temporal Logic (LTL) is the de-facto standard temporal logic for system specification, whose foundational properties have been studied for over five decades. Safety and cosafety properties define notable fragments of LTL, where a…
We prove that the two-variable fragment of first-order logic has the weak Beth definability property. This makes the two-variable fragment a natural logic separating the weak and the strong Beth properties since it does not have the strong…
We study the satisfiability problem of symbolic tree automata and decompose it into the satisfiability problem of the existential first-order theory of the input characters and the existential monadic second-order theory of the indices of…