Related papers: The Complexity of Temporal Logic over the Reals

In this paper, we determine the complexity of the satisfiability problem for various logics obtained by adding numerical quantifiers, and other constructions, to the traditional syllogistic. In addition, we demonstrate the incompleteness of…

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 investigate a version of linear temporal logic whose propositional fragment is G\"odel-Dummett logic (which is well known both as a superintuitionistic logic and a t-norm fuzzy logic). We define the logic using two natural semantics:…

Probabilistic Hoare logic (PHL) is an extension of Hoare logic and is specifically useful in verifying randomized programs. It allows researchers to formally reason about the behavior of programs with stochastic elements, ensuring the…

Evidence often grounds temporal probabilistic relational models over time, which makes reasoning infeasible. To counteract groundings over time and to keep reasoning polynomial by restoring a lifted representation, we present temporal…

To characterize the computational complexity of satisfiability problems for probabilistic and causal reasoning within the Pearl's Causal Hierarchy, arXiv:2305.09508 [cs.AI] introduce a new natural class, named succ-$\exists$R. This class…

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…

Model-checking the alternating-time temporal logics ATL and ATL* with incomplete information is undecidable for perfect recall semantics. However, when restricting to memoryless strategies the model-checking problem becomes decidable. In…

Computational analysis of time-course data with an underlying causal structure is needed in a variety of domains, including neural spike trains, stock price movements, and gene expression levels. However, it can be challenging to determine…

We present a propositional logic to reason about the uncertainty of events, where the uncertainty is modeled by a set of probability measures assigning an interval of probability to each event. We give a sound and complete axiomatization…

We consider quantifier-free spatial logics, designed for qualitative spatial representation and reasoning in AI, and extend them with the means to represent topological connectedness of regions and restrict the number of their connected…

We consider intuitionistic variants of linear temporal logic with `next', `until' and `release' based on expanding posets: partial orders equipped with an order-preserving transition function. This class of structures gives rise to a logic…

Priced timed automata provide a natural model for quantitative analysis of real-time systems and have been successfully applied in various scheduling and planning problems. The optimal reachability problem for linearly-priced timed automata…

We present a probabilistic extension of the description logic $\mathcal{ALC}$ for reasoning about statistical knowledge. We consider conditional statements over proportions of the domain and are interested in the probabilistic-logical…

We prove PSPACE-completeness of all but one problem in a large space of pulling-block problems where the goal is for the agent to reach a target destination. The problems are parameterized by whether pulling is optional, the number of…

We introduce a family of temporal logics to specify the behavior of systems with Zeno behaviors. We extend linear-time temporal logic LTL to authorize models admitting Zeno sequences of actions and quantitative temporal operators indexed by…

We consider probabilistic automata on infinite words with acceptance defined by parity conditions. We consider three qualitative decision problems: (i) the positive decision problem asks whether there is a word that is accepted with…

We study the satisfiability problem for the two-variable first-order logic over structures with one transitive relation. % We show that the problem is decidable in 2-NExpTime for the fragment consisting of formulas where existential…

I consider the following generic scenario: an abstract model M of some 'real' system is only partially presented, or partially known to us, and we have to ensure that the actual system satisfies a given specification, formalised in some…

We consider the model of priced (a.k.a. weighted) timed automata, an extension of timed automata with cost information on both locations and transitions, and we study various model-checking problems for that model based on extensions of…