Checking WECTLK Properties of TRWISs via SMT-based Bounded Model Checking

In this paper, we present a Satisfiability Modulo Theory based (SMT-based) bounded model checking (BMC) method for Timed Real-Weighted Interpreted Systems and for the existential fragment of the Weighted Epistemic Computation Tree Logic. SMT-based bounded model checking consists in translating the existential model checking problem for a modal logic and for a model to the satisfiability problem of a quantifier-free first-order formula. We have implemented the SMT-BMC method and performed the BMC algorithm on Timed Weighted Generic Pipeline Paradigm benchmark. The preliminary experimental results demonstrate the feasibility of the method. To perform the experiments, we used the state of the art SMT-solver Z3

Using multi-agent systems to go beyond temporal patterns verification

A key step in formal verification is the translation of requirements into logic formulae. Various flavours of temporal logic are commonly used in academia and in industry to capture, among others, liveness and safety requirements. In the past two decades there has been a substantial amount of work in the area of verification of extensions of temporal logic. In this column I will provide a high level overview of some work in this area, focussing in particular on the verification of temporal-epistemic properties, showing how temporal-epistemic logics can be used to capture requirements that are common in many concrete systems, and describing a model checker for multi-agent systems called MCMAS

Logic in Cognitive Science: Bridging the Gap between Symbolic and Connectionist Paradigms

What can logic contribute to cognitive science? In the early days of cognitive science, logic was taken to play both a descriptive and a normative role in theories of intelligent behavior. Descriptively, human beings were taken to be fundamentally logical, or rational. Normatively, logic was taken t

SMT-Solvers in Action: Encoding and Solving Selected Problems in NP and EXPTIME

We compare the efficiency of seven modern SMT-solvers for several decision and combinatorial problems: the bounded Post correspondence problem (BPCP), the extended string correction problem (ESCP), and the Towers of Hanoi (ToH) of exponential solutions. For this purpose, we define new original reductions to SMT for all the above problems, and show their complexity. Our extensive experimental results allow for drawing quite interesting conclusions on efficiency and applicability of SMT-solvers depending on the theory used in the encoding

Mechanised Uniform Interpolation for Modal Logics K, GL, and iSL

The uniform interpolation property in a given logic can be understood as the definability of propositional quantifiers. We mechanise the computation of these quantifiers and prove correctness in the Coq proof assistant for three modal logics, namely: (1) the modal logic K, for which a pen-and-paper proof exists; (2) Gödel-Löb logic GL, for which our formalisation clarifies an important point in an existing, but incomplete, sequent-style proof; and (3) intuitionistic strong Löb logic iSL, for which this is the first proof-theoretic construction of uniform interpolants. Our work also yields verified programs that allow one to compute the propositional quantifiers on any formula in this logic

Mechanised Uniform Interpolation for Modal Logics K, GL, and iSL

The uniform interpolation property in a given logic can be understood as the definability of propositional quantifiers. We mechanise the computation of these quantifiers and prove correctness in the Coq proof assistant for three modal logics, namely: (1) the modal logic K, for which a pen-and-paper proof exists; (2) Gödel-Löb logic GL, for which our formalisation clarifies an important point in an existing, but incomplete, sequent-style proof; and (3) intuitionistic strong Löb logic iSL, for which this is the first proof-theoretic construction of uniform interpolants. Our work also yields verified programs that allow one to compute the propositional quantifiers on any formula in this logic

On the computational complexity of ethics: moral tractability for minds and machines

Why should moral philosophers, moral psychologists, and machine ethicists care about computational complexity? Debates on whether artificial intelligence (AI) can or should be used to solve problems in ethical domains have mainly been driven by what AI can or cannot do in terms of human capacities. In this paper, we tackle the problem from the other end by exploring what kind of moral machines are possible based on what computational systems can or cannot do. To do so, we analyze normative ethics through the lens of computational complexity. First, we introduce computational complexity for the uninitiated reader and discuss how the complexity of ethical problems can be framed within Marr’s three levels of analysis. We then study a range of ethical problems based on consequentialism, deontology, and virtue ethics, with the aim of elucidating the complexity associated with the problems themselves (e.g., due to combinatorics, uncertainty, strategic dynamics), the computational methods employed (e.g., probability, logic, learning), and the available resources (e.g., time, knowledge, learning). The results indicate that most problems the normative frameworks pose lead to tractability issues in every category analyzed. Our investigation also provides several insights about the computational nature of normative ethics, including the differences between rule- and outcome-based moral strategies, and the implementation-variance with regard to moral resources. We then discuss the consequences complexity results have for the prospect of moral machines in virtue of the trade-off between optimality and efficiency. Finally, we elucidate how computational complexity can be used to inform both philosophical and cognitive-psychological research on human morality by advancing the moral tractability thesis

Logic-based Technologies for Multi-agent Systems: A Systematic Literature Review

Precisely when the success of artificial intelligence (AI) sub-symbolic techniques makes them be identified with the whole AI by many non-computerscientists and non-technical media, symbolic approaches are getting more and more attention as those that could make AI amenable to human understanding. Given the recurring cycles in the AI history, we expect that a revamp of technologies often tagged as “classical AI” – in particular, logic-based ones will take place in the next few years. On the other hand, agents and multi-agent systems (MAS) have been at the core of the design of intelligent systems since their very beginning, and their long-term connection with logic-based technologies, which characterised their early days, might open new ways to engineer explainable intelligent systems. This is why understanding the current status of logic-based technologies for MAS is nowadays of paramount importance. Accordingly, this paper aims at providing a comprehensive view of those technologies by making them the subject of a systematic literature review (SLR). The resulting technologies are discussed and evaluated from two different perspectives: the MAS and the logic-based ones