Bounded Model Checking (BMC) searches for counterexamples to a property φ with a bounded length k. If no such counterexample is found, k is increased. This process terminates when k exceeds the completeness threshold CT (i.e., k is sufficiently large to ensure that no counterexample exists) or when the SAT procedure exceeds its time or memory bounds. However, the completeness threshold is too l...

We introduce Multimodal Logics of Normative Systems as a contribution to the development of a general logical framework for reasoning about normative systems over logics for Multi-Agent Systems. Given a multimodal logicL, for every modality 2i and normative system η, we expand the language adding a new modality 2ηi with the intended meaning of 2 η i φ being ”φ is obligatory in the context of th...

σz = 1 0 0 −1 basis. We treat the 2-qubit Swap gate ↑↑ ↑↓ ↓↑ ↓↓ ↑↑ 1 0 0 0 ↑↓ 0 0 1 0 ↓↑ 0 1 0 0 ↓↓ 0 0 0 1 as inherent to the circuit model, i.e. the timelines of qubits can be permuted. Thus, for example, a given 2-qubit gate can always be applied to any pair of qubits and in either order. The proof of “universality” of a given set of gates, i.e. universality for the class BQP (polynomial tim...

Synthesis techniques take realizable Linear Temporal Logic specifications and produce correct circuits that implement the specifications. The generated circuits can be used directly, or as miters that check the correctness of a logic design. Typically, those techniques generate non-deterministic finite state automata, which can be determinized at a possibly exponential cost. Recent results show...

Liveness temporal properties state that something “good” eventually happens, e.g., every request is eventually granted. In Linear Temporal Logic (LTL), there is no a priori bound on the “wait time” for an eventuality to be fulfilled. That is, Fθ asserts that θ holds eventually, but there is no bound on the time when θ will hold. This is troubling, as designers tend to interpret an eventuality F...

Automated planning (Ghallab, Nau, and Traverso 2004) is the artificial intelligence field that studies the process of reasoning about actions and goals, seeking for implementation of planners. Essentially, a planner is an algorithm that synthesizes a plan of actions by analyzing a formal specification of the environment’s dynamic and the agent’s goal. Since the trajectory of a plan have tempora...

Many proposals for logic-based formalizations of argumentation consider an argument as a pair (Φ, α), where the support Φ is understood as a minimal consistent subset of a given knowledge base which has to entail the claim α. In most scenarios, arguments are given in the full language of classical propositional logic which makes reasoning in such frameworks a computationally costly task. For in...

We add a limited but useful form of quantification to Coalition Logic, a popular formalism for reasoning about cooperation in game-like multi-agent systems. The basic constructs of Quantified Coalition Logic (QCL) allow us to express such properties as “every coalition satisfying property P can achieve φ” and “there exists a coalition C satisfying property P such that C can achieve φ”. We give ...

Abstract. We present a model checking algorithm for CTL (and full CTL) which uses an iterative abstraction refinement strategy. In each iteration we call a standard model checker for the abstract models i. If i does not satisfy Φ we refine the abstract model i yielding another abstract model i 1 and (re-)call the model checker to i 1. Otherwise the formula holds for the original system . Our al...

We address the problem of automatically identifying what local properties the agents of a Cyber Physical System have to satisfy to guarantee a global required property φ. To enrich the picture, we consider properties where, besides qualitative requirements on the actions to be performed, we assume a weight associated with them: quantitative properties are specified through a weighted modal-logi...