Related papers: A Probabilistic Higher-order Fixpoint Logic
Verification of higher-order probabilistic programs is a challenging problem. We present a verification method that supports several quantitative properties of higher-order probabilistic programs. Usually, extending verification methods to…
First-order linear temporal logic (FOLTL) is a flexible and expressive formalism capable of naturally describing complex behaviors and properties. Although the logic is in general highly undecidable, the idea of using it as a specification…
In this paper, we explain how the connection between higher-order model-checking and linear logic recently exhibited by the authors leads to a new and conceptually enlightening proof of the selection problem originally established by…
A continuous-time Markov chain (CTMC) execution is a continuous class of probability distributions over states. This paper proposes a probabilistic linear-time temporal logic, namely continuous-time linear logic (CLL), to reason about the…
Given a class of finite models we would like to expand each model (allowing new elements but the old universe is a separate sort), making the expressive power of LFP (least fix point logic) and PFP (inductive logic) similar while not…
Deficiency in expressive power of the first-order logic has led to developing its numerous extensions by fixed point operators, such as Least Fixed-Point (LFP), inflationary fixed-point (IFP), partial fixed-point (PFP), etc. These logics…
This paper studies Linear Temporal Logic over Finite Traces (LTLf) where proposition letters are replaced with first-order formulas interpreted over arbitrary theories, in the spirit of Satisfiability Modulo Theories. The resulting logic,…
A key problem in the application of first-order probabilistic methods is the enormous size of graphical models they imply. The size results from the possible worlds that can be generated by a domain of objects and relations. One of the…
The problem of determining whether a probabilistic program terminates almost surely (i.e.~with probability one) is undecidable, and actually $\Pi^0_2$-complete. For this reason, a growing literature has explored classes of programs for…
Probabilistic Computation Tree Logic (PCTL) and Continuous Stochastic Logic (CSL) are often used to describe specifications of probabilistic properties for discrete time and continuous time, respectively. In PCTL and CSL, the possibility of…
Possibilistic computation tree Logic (PoCTL) is one kind of branching temporal logic combined with uncertain information in possibility theory, which was introduced in order to cope with the systematic verification on systems with uncertain…
Parametric Markov chains have been introduced as a model for families of stochastic systems that rely on the same graph structure, but differ in the concrete transition probabilities. The latter are specified by polynomial constraints for…
We investigate the expressive power of the two main kinds of program logics for complex, non-regular program properties found in the literature: those extending propositional dynamic logic (PDL), and those extending the modal mu-calculus.…
Safety-critical infrastructures must operate in a safe and reliable way. Fault tree analysis is a widespread method used for risk assessment of these systems: fault trees (FTs) are required by, e.g., the Federal Aviation Administration and…
We investigate the decidability of the definability problem for fragments of first order logic over finite words enriched with modular predicates. Our approach aims toward the most generic statements that we could achieve, which…
We propose a novel logic, called Frame Logic (FL), that extends first-order logic (with recursive definitions) using a construct Sp(.) that captures the implicit supports of formulas -- the precise subset of the universe upon which their…
Logical formalisms such as first-order logic (FO) and fixpoint logic (FP) are well suited to express in a declarative manner fundamental graph functionalities required in distributed systems. We show that these logics constitute good…
The overall goal of this paper is to investigate the theoretical foundations of algorithmic verification techniques for first order linear logic specifications. The fragment of linear logic we consider in this paper is based on the linear…
We study the problem of formalizing and checking probabilistic hyperproperties for models that allow nondeterminism in actions. We extend the temporal logic \HyperPCTL, which has been previously introduced for discrete-time Markov chains,…
We introduce an extension of fixed-point logic ($\mathsf{FP}$) with a group-order operator ($\mathsf{ord}$), that computes the size of a group generated by a definable set of permutations. This operation is a generalization of the rank…