Like any other logical theory, domain descriptions in reasoning about actions may evolve, and thus need revision methods to adequately accommodate new information about the behavior of actions. The present work is about changing action domain descriptions in propositional dynamic logic. Its contribution is threefold: first we revisit the semantics of action theory contraction that has been done in previous work, giving more robust operators that express minimal change based on a notion of distance between Kripke-models. Second we give algorithms for syntactical action theory contraction and establish their correctness w.r.t. our semantics. Finally we state postulates for action theory contraction and assess the behavior of our operators w.r.t. them. Moreover, we also address the revision counterpart of action theory change, showing that it benefits from our semantics for contraction.
Herzig al @cite_39 define a method for action theory contraction that, despite the similarity with the current work and the common underlying motivations, is more limited than the present constructions. First, with the referred approach we do not get minimal change. For example, in the referred work the operator for contracting executability laws is such that in the resulting theory the modified set of executabilities is given by [ - = ( i ) : i ] which, according to its semantics, gives theories among whose models are those resulting from removing arrows from all @math -worlds. A similar comment can be made contraction of effect laws.
@cite_39
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In this work we address the problem of elaborating domain descriptions (alias action theories), in particular those that are expressed in dynamic logic. We define a general method based on contraction of formulas in a version of propositional dynamic logic with a solution to the frame problem. We present the semantics of our theory change and define syntactical operators for contracting a domain description. We establish soundness and completeness of the operators w.r.t. the semantics for descriptions that satisfy a principle of modularity that we have defined in previous work. A theory of discrimination which assumes that subjects compare psychological values evoked by a stimulus to a subjective referent is proposed. Momentary differences between psychological values for the stimulus and the referent are accumulated over time until one or the other of two response thresholds is first exceeded. The theory is analyzed as a random walk bounded between two absorbing barriers. A general solution to response conditioned expected response times is computed and the important role played by the moment generating function (mgf) for increments to the random walk is examined. From considerations of the mgf it is shown that unlike other random walk models [Stone, 1960; Laming, 1968] the present theory does not imply that response conditioned mean correct and error times must be equal. For two fixed stimuli and a fixed referent it is shown that by controlling values of response thresholds, subjects can produce Receiver Operating Characteristics similar or identical to those predicted by Signal Detection Theory, High Threshold Theory, or Low Threshold Theory. This paper outlines a new theory of plan recognition that is significantly more powerful than previous approaches. Concurrent actions, shared steps between actions, and disjunctive information are all handled. The theory allows one to draw conclusions based on the class of possible plans being performed, rather than having to prematurely commit to a single interpretation. The theory employs circumscription to transform a first-order theory of action into an action taxonomy, which can be used to logically deduce the complex action(s) an agent is performing. This paper describes a change theory based on abductive reasoning. We take the AGM postulates for revisions, expansions and contractions, and Katsuno and Mendelzon postulates for updates and incorporate abduction into them. A key feature of the theory is that presents a unified view of standard change operators and abductive change operators rather than a new and independent change theory for abductive changes. Abductive operators reduce to standard change operators in the limiting cases. Active inference is emerging as a possible unifying theory ofperception and action in cognitive and computational neuro-science. On this theory, perception is a process of inferringthe causes of sensory data by minimising the error betweenactual sensations and those predicted by an innergenerative(probabilistic) model. Action on the other hand is drawn as aprocess that modifies the world such that the consequent sen-sory input meets expectations encoded in the same internalmodel. These two processes, inferring properties of the worldand inferring actions needed to meet expectations, close thesensory motor loop and suggest a deep symmetry betweenaction and perception. In this work we present a simpleagent-based model inspired by this new theory that offers in-sights on some of its central ideas. Previous implementationsof active inference have typically examined a “perception-oriented” view of this theory, assuming that agents are en-dowed with a detailed generative model of their surround-ing environment. In contrast, we present an “action-oriented”solution showing how adaptive behaviour can emerge evenwhen agents operate with a simple model which bears littleresemblance to their environment. We examine how variousparameters of this formulation allow phototaxis and presentan example of a different, “pathological” behaviour. This paper extends earlier work by its authors on formal aspects of the processes of contracting a theory to eliminate a proposition and revising a theory to introduce a proposition. In the course of the earlier work, Gardenfors developed general postulates of a more or less equational nature for such processes, whilst Alchourron and Makinson studied the particular case of contraction functions that are maximal, in the sense of yielding a maximal subset of the theory (or alternatively, of one of its axiomatic bases), that fails to imply the proposition being eliminated. In the present paper, the authors study a broader class, including contraction functions that may be less than maximal. Specifically, they investigate “partial meet contraction functions”, which are defined to yield the intersection of some nonempty family of maximal subsets of the theory that fail to imply the proposition being eliminated. Basic properties of these functions are established: it is shown in particular that they satisfy the Gardenfors postulates, and moreover that they are sufficiently general to provide a representation theorem for those postulates. Some special classes of partial meet contraction functions, notably those that are “relational” and “transitively relational”, are studied in detail, and their connections with certain “supplementary postulates” of Gardenfors investigated, with a further representation theorem established. In this article we investigate the relation between consequences of Dirichlet boundary conditions (momenta noncommutativity and parameters of the effective theory) and background fields of fermionic T-dual theory. We impose Dirichlet boundary conditions on the endpoints of the open string propagating in background of type IIB superstring theory. We showed that on the solution of the boundary conditions the momenta become noncommutative, while the coordinates commute. Fermionic Tduality is also introduced and its relation to noncommutativity is considered. We use compact notation so that type IIB superstring formally gets the form of the bosonic one with Grassman variables. Then momenta noncommutativity parameters are fermionic T-dual fields. The effective theory, the initial theory on the solution of boundary conditions, is bilinear in the effective coordinates, odd under world-sheet parity transformation. The effective metric is equal to the initial one and terms with the effective Kalb-Ramond field vanish. Recent research on reasoning about action has shown that the traditional logic form of domain constraints is problematic to represent ramifications of actions that are related to causality of domains. To handle this problem properly, as proposed by some researchers, it is necessary to describe causal relations of domains explicitly in action theories. In this paper, we address this problem from a new point of view. Specifically, unlike other researchers viewing causal relations as some kind of inference rules, we distinguish causal relations between defeasible and non-defeasible cases. It turns out that a causal theory in our formalism can be specified by using Reiter's default logic. Based on this idea, we propose a causality-based minimal change approach for representing effects of actions, and argue that our approach provides more plausible solutions for the ramification and qualification problems compared with other related work. We also describe a logic programming approximation to compute causal theories of actions which provides an implementational basis for our approach. In this paper, we introduce a new concept of generalized partial meet contraction for contracting a sentence from a belief base. We show that a special case of belief dynamics, referred to as knowledge base dynamics, where certain part of the belief base is declared to be immutable, has interesting connections with abduction, thus enabling us to use abductive procedures to realize contractions. Finally, an important application of knowledge base dynamics in providing an axiomatic characterization for deleting view atoms from databases is discussed in detail. We investigate general probabilistic theories in which every mixed state has a purification, unique up to reversible channels on the purifying system. We show that the purification principle is equivalent to the existence of a reversible realization of every physical process, that is, to the fact that every physical process can be regarded as arising from a reversible interaction of the system with an environment, which is eventually discarded. From the purification principle we also construct an isomorphism between transformations and bipartite states that possesses all structural properties of the Choi-Jamiolkowski isomorphism in quantum theory. Such an isomorphism allows one to prove most of the basic features of quantum theory, like, e.g., existence of pure bipartite states giving perfect correlations in independent experiments, no information without disturbance, no joint discrimination of all pure states, no cloning, teleportation, no programming, no bit commitment, complementarity between correctable channels and deletion channels, characterization of entanglement-breaking channels as measure-and-prepare channels, and others, without resorting to the mathematical framework of Hilbert spaces. We extend the 0-approximation of sensing actions and incomplete information in Son and Baral (2001) to action theories with static causal laws and prove its soundness with respect to the possible world semantics. We also show that the conditional planning problem with respect to this approximation is NP-complete. We then present an answer set programming based conditional planner, called ASCP, that is capable of generating both conformant plans and conditional plans in the presence of sensing actions, incomplete information about the initial state, and static causal laws. We prove the correctness of our implementation and argue that our planner is sound and complete with respect to the proposed approximation. Finally, we present experimental results comparing ASCP to other planners. Abstract This paper presents a logical approach to nonmonotonic reasoning based on the notion of a nonmonotonic consequence relation. A conditional knowledge base, consisting of a set of conditional assertions of the type if … then … , represents the explicit defeasible knowledge an agent has about the way the world generally behaves. We look for a plausible definition of the set of all conditional assertions entailed by a conditional knowledge base. In a previous paper, Kraus and the authors defined and studied preferential consequence relations. They noticed that not all preferential relations could be considered as reasonable inference procedures. This paper studies a more restricted class of consequence relations, rational relations. It is argued that any reasonable nonmonotonic inference procedure should define a rational relation. It is shown that the rational relations are exactly those that may be represented by a ranked preferential model, or by a (nonstandard) probabilistic model. The rational closure of a conditional knowledge base is defined and shown to provide an attractive answer to the question of the title. Global properties of this closure operation are proved: it is a cumulative operation. It is also computationally tractable. This paper assumes the underlying language is propositional. The paper introduces an action recognition framework that uses concepts from the theory of chaotic systems to model and analyze nonlinear dynamics of human actions. Trajectories of reference joints are used as the representation of the non-linear dynamical system that is generating the action. Each trajectory is then used to reconstruct a phase space of appropriate dimension by employing a delay-embedding scheme. The properties of the reconstructed phase space are captured in terms of dynamical and metric invariants that include Lyapunov exponent, correlation integral and correlation dimension. Finally, the action is represented by a feature vector which is a combination of these invariants over all the reference trajectories. Our contributions in this paper include :1) investigation of the appropriateness of theory of chaotic systems for human action modelling and recognition, 2) a new set of features to characterize nonlinear dynamics of human actions, 3) experimental validation of the feasibility and potential merits of carrying out action recognition using methods from theory of chaotic systems. This paper studies a generalized class of restless multi-armed bandits with hidden states and allow cumulative feedback, as opposed to the conventional instantaneous feedback. We call them lazy restless bandits (LRBs) as the events of decision making are sparser than the events of state transition. Hence, feedback after each decision event is the cumulative effect of the following state transition events. The states of arms are hidden from the decision maker and rewards for actions are state dependent. The decision maker needs to choose one arm in each decision interval, such that the long-term cumulative reward is maximized. As the states are hidden, the decision maker maintains and updates its belief about them. It is shown that LRBs admit an optimal policy which has threshold structure in belief space. The Whittle-index policy for solving the LRB problem is analyzed; indexability of LRBs is shown. Further, the closed-form index expressions are provided for two sets of special cases; for more general cases, an algorithm for index computation is provided. An extensive simulation study is presented; Whittle-index, modified Whittle-index, and myopic policies are compared. The Lagrangian relaxation of the problem provides an upper bound on the optimal value function; it is used to assess the degree of sub-optimality various policies. We study an evolving spatial network in which sequentially arriving vertices are joined to existing vertices at random according to a rule that combines preference according to degree with preference according to spatial proximity. We investigate phase transitions in graph structure as the relative weighting of these two components of the attachment rule is varied. Previous work of one of the authors showed that when the geometric component is weak, the limiting degree sequence of the resulting graph coincides with that of the standard Barab 'asi--Albert preferential attachment model. We show that at the other extreme, in the case of a sufficiently strong geometric component, the limiting degree sequence coincides with that of a purely geometric model, the on-line nearest-neighbour graph, which is of interest in its own right and for which we prove some extensions of known results. We also show the presence of an intermediate regime, in which the behaviour differs significantly from both the on-line nearest-neighbour graph and the Barab 'asi--Albert model; in this regime, we obtain a stretched exponential upper bound on the degree sequence. Our results lend some mathematical support to simulation studies of Manna and Sen, while proving that the power law to stretched exponential phase transition occurs at a different point from the one conjectured by those authors. The present notes are intended to present a detailed review of the existing results in dissipative kinetic theory which make use of the contraction properties of two main families of probability metrics: optimal mass transport and Fourier-based metrics. The first part of the notes is devoted to a self-consistent summary and presentation of the properties of both probability metrics, including new aspects on the relationships between them and other metrics of wide use in probability theory. These results are of independent interest with potential use in other contexts in Partial Differential Equations and Probability Theory. The second part of the notes makes a different presentation of the asymptotic behavior of Inelastic Maxwell Models than the one presented in the literature and it shows a new example of application: particle's bath heating. We show how starting from the contraction properties in probability metrics, one can deduce the existence, uniqueness and asymptotic stability in classical spaces. A global strategy with this aim is set up and applied in two dissipative models. Using the theory of group action, we first introduce the concept of the automorphism group of an exponential family or a graphical model, thus formalizing the general notion of symmetry of a probabilistic model. This automorphism group provides a precise mathematical framework for lifted inference in the general exponential family. Its group action partitions the set of random variables and feature functions into equivalent classes (called orbits) having identical marginals and expectations. Then the inference problem is effectively reduced to that of computing marginals or expectations for each class, thus avoiding the need to deal with each individual variable or feature. We demonstrate the usefulness of this general framework in lifting two classes of variational approximation for MAP inference: local LP relaxation and local LP relaxation with cycle constraints; the latter yields the first lifted inference that operate on a bound tighter than local constraints. Initial experimental results demonstrate that lifted MAP inference with cycle constraints achieved the state of the art performance, obtaining much better objective function values than local approximation while remaining relatively efficient. We prove a law of large numbers for a class of ballistic, multidimensional random walks in random environments where the environment satisfies appropriate mixing conditions, which hold when the environment is a weak mixing field in the sense of Dobrushin and Shlosman. Our result holds if the mixing rate balances moments of some random times depending on the path. It applies in the nonnestling case, but we also provide examples of nestling walks that satisfy our assumptions. The derivation is based on an adaptation, using coupling, of the regeneration argument of Sznitman and Zerner. It is shown that it is possible to introduce determinism into quantum mechanics by tracing the probabilities in the Born rules back to pseudorandomness in the absolute phase constants of the wave functions. Each wave function is conceived to contain an individual phase factor exp(iα). In an ensemble of systems the phase constants α are taken to be pseudorandom numbers. A reduction process (collapse), independent of any measurement, is conceived to be a spatial contraction of two wavepackets when they meet and satisfy a certain criterion. The criterion depends on the phase constants of both wavepackets. The measurement apparatus fans out the incoming wavepacket into spatially separated eigenpackets of the observable and a reduction associates the point of contraction with an eigenvalue of the observable. The theory is nonlocal and contextual. We start from Reiter’s solution to the frame problem in terms of successor state axioms and Scherl and Levesque’s extension to knowledge, as formulated by Lakemeyer and Levesque in their logic ES.While it was believed up to now that quantification over actions is a characteristic feature of Reiter’s solution, we here show that for a reasonably large subset of Reiter’s basic action theories one can do without.We do so by recasting restricted basic action theories in a propositional modal logic, viz. dynamic epistemic logic with public announcements and public assignments.