Towards Understanding Reasoning Complexity in Practice

Although the computational complexity of the logic underlying the standard OWL 2 for the Web Ontology Language (OWL) appears discouraging for real applications, several contributions have shown that reasoning with OWL ontologies is feasible in practice. It turns out that reasoning in practice is often far less complex than is suggested by the established theoretical complexity bound, which reflects the worstcase scenario. State-of-the reasoners like FACT++, HERMIT, PELLET and RACER have demonstrated that, even with fairly expressive fragments of OWL 2, acceptable performances can be achieved. However, it is still not well understood why reasoning is feasible in practice and it is rather unclear how to study this problem. In this paper, we suggest first steps that in our opinion could lead to a better understanding of practical complexity. We also provide and discuss some initial empirical results with HERMIT on prominent ontologie

Task-set switching with natural scenes: Measuring the cost of deploying top-down attention

In many everyday situations, we bias our perception from the top down, based on a task or an agenda. Frequently, this entails shifting attention to a specific attribute of a particular object or scene. To explore the cost of shifting top-down attention to a different stimulus attribute, we adopt the task-set switching paradigm, in which switch trials are contrasted with repeat trials in mixed-task blocks and with single-task blocks. Using two tasks that relate to the content of a natural scene in a gray-level photograph and two tasks that relate to the color of the frame around the image, we were able to distinguish switch costs with and without shifts of attention. We found a significant cost in reaction time of 23–31 ms for switches that require shifting attention to other stimulus attributes, but no significant switch cost for switching the task set within an attribute. We conclude that deploying top-down attention to a different attribute incurs a significant cost in reaction time, but that biasing to a different feature value within the same stimulus attribute is effortless

PDL with Negation of Atomic Programs

Propositional dynamic logic (PDL) is one of the most succesful variants of modal logic. To make it even more useful for applications, many extensions of PDL have been considered in the literature. A very natural and useful such extension is with negation of programs. Unfortunately, it is long-known that reasoning with the resulting logic is undecidable. In this paper, we consider the extension of PDL with negation of atomic programs, only. We argue that this logic is still useful, e.g. in the context of description logics, and prove that satisfiability is decidable and EXPTIME-complete using an approach based on Büchi tree automata

Quantitative temporal logics over the reals: PSpace and below

AbstractIn many cases, the addition of metric operators to qualitative temporal logics (TLs) increases the complexity of satisfiability by at least one exponential: while common qualitative TLs are complete for NP or PSpace, their metric extensions are often ExpSpace-complete or even undecidable. In this paper, we exhibit several metric extensions of qualitative TLs of the real line that are at most PSpace-complete, and analyze the transition from NP to PSpace for such logics. Our first result is that the logic obtained by extending since-until logic of the real line with the operators ‘sometime within n time units in the past/future’ is still PSpace-complete. In contrast to existing results, we also capture the case where n is coded in binary and the finite variability assumption is not made. To establish containment in PSpace, we use a novel reduction technique that can also be used to prove tight upper complexity bounds for many other metric TLs in which the numerical parameters to metric operators are coded in binary. We then consider metric TLs of the reals that do not offer any qualitative temporal operators. In such languages, the complexity turns out to depend on whether binary or unary coding of parameters is assumed: satisfiability is still PSpace-complete under binary coding, but only NP-complete under unary coding

Quantitative Temporal Logics: PSpace and below

Often the addition of metric operators to qualitative temporal logics leads to an increase of the complexity of satisfiability by at least one exponential. In this paper, we exhibit a number of metric extensions of qualitative temporal logics of the real line that do not lead to an increase in computational complexity. The main result states that the language obtained by extending since/until logic of the real line with the operators 'sometime within n time units', n coded in binary, is PSpace-complete even without the finite variability assumption. Without qualitative temporal operators the complexity of this language turns out to depend on whether binary or unary coding of parameters is assumed: it is still PSpace-hard under binary coding but in NP under unary coding

Biogenesis of β-barrel membrane proteins in bacteria and eukaryotes: evolutionary conservation and divergence

Membrane-embedded β-barrel proteins span the membrane via multiple amphipathic β-strands arranged in a cylindrical shape. These proteins are found in the outer membranes of Gram-negative bacteria, mitochondria and chloroplasts. This situation is thought to reflect the evolutionary origin of mitochondria and chloroplasts from Gram-negative bacterial endosymbionts. β-barrel proteins fulfil a variety of functions; among them are pore-forming proteins that allow the flux of metabolites across the membrane by passive diffusion, active transporters of siderophores, enzymes, structural proteins, and proteins that mediate protein translocation across or insertion into membranes. The biogenesis process of these proteins combines evolutionary conservation of the central elements with some noticeable differences in signals and machineries. This review summarizes our current knowledge of the functions and biogenesis of this special family of proteins

Reasoning About the Transfer of Control

We present DCL-PC: a logic for reasoning about how the abilities of agents and coalitions of agents are altered by transferring control from one agent to another. The logical foundation of DCL-PC is CL-PC, a logic for reasoning about cooperation in which the abilities of agents and coalitions of agents stem from a distribution of atomic Boolean variables to individual agents -- the choices available to a coalition correspond to assignments to the variables the coalition controls. The basic modal constructs of DCL-PC are of the form coalition C can cooperate to bring about phi. DCL-PC extends CL-PC with dynamic logic modalities in which atomic programs are of the form agent i gives control of variable p to agent j; as usual in dynamic logic, these atomic programs may be combined using sequence, iteration, choice, and test operators to form complex programs. By combining such dynamic transfer programs with cooperation modalities, it becomes possible to reason about how the power of agents and coalitions is affected by the transfer of control. We give two alternative semantics for the logic: a direct semantics, in which we capture the distributions of Boolean variables to agents; and a more conventional Kripke semantics. We prove that these semantics are equivalent, and then present an axiomatization for the logic. We investigate the computational complexity of model checking and satisfiability for DCL-PC, and show that both problems are PSPACE-complete (and hence no worse than the underlying logic CL-PC). Finally, we investigate the characterisation of control in DCL-PC. We distinguish between first-order control -- the ability of an agent or coalition to control some state of affairs through the assignment of values to the variables under the control of the agent or coalition -- and second-order control -- the ability of an agent to exert control over the control that other agents have by transferring variables to other agents. We give a logical characterisation of second-order control

Strategic logics : complexity, completeness and expressivity

by transferring normative attributes from an agent to another. Such interactions are called delegation. Formal models of delegation and control were studied in, e.g., [189, 149, 191]. In this work, we consider the scenario where agents delegate control over propositions to other agents. The distinction between controllable and uncontrollable propositions stems from areas like discrete event systems and control theory, where, e.g., Boutilier [39] studied control in the context of deontic logic. Control and controllable propositions were also studied in [52, 66, 249, 248]. We now give an overview of the thesis. The main purpose of Chapter 2 is to introduce basic concepts and notation and to review relevant literature. The first section presents a brief survey on modal logic. Then, in sections 2.2, 2.3 and 2.4, we introduce epistemic, temporal and strategic modal logics and state known results that characterise their expressivity and computational complexity. In particular, we consider variants of ATL as extensions of branching-time logics. With such ATL-like logics we can describe dynamic multi-agent interactions. In Section 2.5, we discuss extensions of ATL with epistemic notions. Additionally, we suggest a framework for memory-bounded strategic reasoning. In particular, we introduce an epistemic variant of ATL that accounts for agents with limited memory resources as this case was neglected in the literature to date. In Chapter 3, we investigate the computational complexity of ATL and its epistemic extension ATEL. We show in detail how 'the complexity of the satisfiability problem for both logics can be settled at ExpTIME-complete. The part of the chapter about ATL is based on the paper 'ATL Satisfiability is Indeed ExpTIME-COmplete' by Walther, Lutz, Wolter and Wooldridge in the Journal of Logic and Computation, 2006 (265)' and the part about ATEL is based on the paper 'ATEL with Common and Distributed Knowledge is ExpTime-Complete' by Walther which was presented at the 4th Workshop on Methods for Modalities, Humbolt University, Berlin, December 1-2, 2005 [264]. In Chapter 4, we aim to extend the expressiveness of ATL without increasing its computational complexity. We introduce explicit names for strategies in the object language and extend modal operators with the possibility to bind agents to strategy names. In this way, we can fix the decisions of agents that possibly belong to several coalitions. By identifying the behaviqur of agents, we can reason about the effects of agents changing coalitions. Dynamic coalitions provide more flexibility to adapt abilities to a changing environment. We investigate the expressivity of the resulting logic ATLES and compare it to ATL and ATL*. Moreover, we formulate two model checking problems for ATLES and investigate their complexity as well as the complexity of the satisfiability problem for ATLES. Additionally, we present a complete axiomatisation. This chapter is based on the paper 'Alternating-time Temporal Logic with Explicit Strategies' by Walther, van der Hoek and Wooldridge which is going to presented at the 11th Conference on Theoretical Aspects of Rationality and Knowledge (TARK), Brussels, Belgium, June 25-27, 2007 [266]