Semantics for possibilistic answer set programs: uncertain rules versus rules with uncertain conclusions

Although Answer Set Programming (ASP) is a powerful framework for declarative problem solving, it cannot in an intuitive way handle situations in which some rules are uncertain, or in which it is more important to satisfy some constraints than others. Possibilistic ASP (PASP) is a natural extension of ASP in which certainty weights are associated with each rule. In this paper we contrast two different views on interpreting the weights attached to rules. Under the first view, weights reflect the certainty with which we can conclude the head of a rule when its body is satisfied. Under the second view, weights reflect the certainty that a given rule restricts the considered epistemic states of an agent in a valid way, i.e. it is the certainty that the rule itself is correct. The first view gives rise to a set of weighted answer sets, whereas the second view gives rise to a weighted set of classical answer sets.

Characterizing and Extending Answer Set Semantics using Possibility Theory

Answer Set Programming (ASP) is a popular framework for modelling combinatorial problems. However, ASP cannot be used easily for reasoning about uncertain information. Possibilistic ASP (PASP) is an extension of ASP that combines possibilistic logic and ASP. In PASP a weight is associated with each rule, whereas this weight is interpreted as the certainty with which the conclusion can be established when the body is known to hold. As such, it allows us to model and reason about uncertain information in an intuitive way. In this paper we present new semantics for PASP in which rules are interpreted as constraints on possibility distributions. Special models of these constraints are then identified as possibilistic answer sets. In addition, since ASP is a special case of PASP in which all the rules are entirely certain, we obtain a new characterization of ASP in terms of constraints on possibility distributions. This allows us to uncover a new form of disjunction, called weak disjunction, that has not been previously considered in the literature. In addition to introducing and motivating the semantics of weak disjunction, we also pinpoint its computational complexity. In particular, while the complexity of most reasoning tasks coincides with standard disjunctive ASP, we find that brave reasoning for programs with weak disjunctions is easier.

Using Answer Set Programming for Solving Boolean Games

Boolean games are a framework for reasoning about the rational behaviour of agents, whose goals are formalized using propositional formulas. They offer an attractive alternative to normal-form games, because they allow for a more intuitive and more compact encoding. Unfortunately, however, there is currently no general, tailor-made method available to compute the equilibria of Boolean games. In this paper, we introduce a method for finding the pure Nash equilibria based on disjunctive answer set programming. Our method is furthermore capable of finding the core elements and the Pareto optimal equilibria, and can easily be modified to support other forms of optimality, thanks to the declarative nature of disjunctive answer set programming. Experimental results clearly demonstrate the effectiveness of the proposed method.

Possibilistic Answer Set Programming Revisited

Possibilistic answer set programming (PASP) extends answer set programming (ASP) by attaching to each rule a degree of certainty. While such an extension is important from an application point of view, existing semantics are not well-motivated, and do not always yield intuitive results. To develop a more suitable semantics, we first introduce a characterization of answer sets of classical ASP programs in terms of possibilistic logic where an ASP program specifies a set of constraints on possibility distributions. This characterization is then naturally generalized to define answer sets of PASP programs. We furthermore provide a syntactic counterpart, leading to a possibilistic generalization of the well-known Gelfond-Lifschitz reduct, and we show how our framework can readily be implemented using standard ASP solvers.

Communicating Answer Set Programs

Answer set programming is a form of declarative programming that has proven very successful in succinctly formulating and solving complex problems. Although mechanisms for representing and reasoning with the combined answer set programs of multiple agents have already been proposed, the actual gain in expressivity when adding communication has not been thoroughly studied. We show that allowing simple programs to talk to each other results in the same expressivity as adding negation-as-failure. Furthermore, we show that the ability to focus on one program in a network of simple programs results in the same expressivity as adding disjunction in the head of the rules.

Towards Possibilistic Fuzzy Answer Set Programming

Fuzzy answer set programming (FASP) is a generalization of answer set programming to continuous domains. As it can not readily take uncertainty into account, however, FASP is not suitable as a basis for approximate reasoning and cannot easily be used to derive conclusions from imprecise information. To cope with this, we propose an extension of FASP based on possibility theory. The resulting framework allows us to reason about uncertain information in continuous domains, and thus also about information that is imprecise or vague. We propose a syntactic procedure, based on an immediate consequence operator, and provide a characterization in terms of minimal models, which allows us to straightforwardly implement our framework using existing FASP solvers.

What defines a geochemical map? Implications for environmental assessment.

The environmental quality of land is often assessed by the calculation of threshold values which aim to differentiate between concentrations of elements based on whether the soils are in residential or industrial sites. In Europe, for example, soil guideline values exist for agricultural and grazing land. A threshold is often set to differentiate between concentrations of the element that naturally occur in the soil and concentrations that result from diffuse anthropogenic sources. Regional geochemistry and, in particular, single component geochemical maps are increasingly being used to determine these baseline environmental assessments. The key question raised in this paper is whether the geochemical map can provide an accurate interpretation on its own. Implicit is the thought that single component geochemical maps represent absolute abundances. However,because of the compositional (closed) nature of the data univariate geochemical maps cannot be compared directly with one another.. As a result, any interpretation based on them is vulnerable to spurious correlation problems. What does this mean for soil geochemistry mapping, baseline quality documentation, soil resource assessment or risk evaluation? Despite the limitation of relative abundances, individual raw geochemical maps are deemed fundamental to several applications of geochemical maps including environmental assessments. However, element toxicity is related to its bioavailable concentration, which is lowered if its source is mixed with another source. Elements interact, for example under reducing conditions with iron oxides, its solid state is lost and arsenic becomes soluble and mobile. Both of these matters may be more adequately dealt with if a single component map is not interpreted in isolation to determine baseline and threshold assessments. A range of alternative compositionally compliant representations based on log-ratio and log-contrast approaches are explored to supplement the classical single component maps for environmental assessment. Case study examples are shown based on the Tellus soil geochemical dataset, covering Northern Ireland and the results of in vitro oral bioaccessibility testing carried out on a sub-set of archived Tellus Survey shallow soils following the Unified BARGE (Bioaccessibility Research Group of Europe).

Inferring and Exploiting Categories for Next Location Prediction

Predicting the next location of a user based on their previous visiting pattern is one of the primary tasks over data from location based social networks (LBSNs) such as Foursquare. Many different aspects of these so-called “check-in” profiles of a user have been made use of in this task, including spatial and temporal information of check-ins as well as the social network information of the user. Building more sophisticated prediction models by enriching these check-in data by combining them with information from other sources is challenging due to the limited data that these LBSNs expose due to privacy concerns. In this paper, we propose a framework to use the location data from LBSNs, combine it with the data from maps for associating a set of venue categories with these locations. For example, if the user is found to be checking in at a mall that has cafes, cinemas and restaurants according to the map, all these information is associated. This category information is then leveraged to predict the next checkin location by the user. Our experiments with publicly available check-in dataset show that this approach improves on the state-of-the-art methods for location prediction.

Answer set programs with optional rules: a possibilistic approach

Many problems in artificial intelligence can be encoded as answer set programs (ASP) in which some rules are uncertain. ASP programs with incorrect rules may have erroneous conclusions, but due to the non-monotonic nature of ASP, omitting a correct rule may also lead to errors. To derive the most certain conclusions from an uncertain ASP program, we thus need to consider all situations in which some, none, or all of the least certain rules are omitted. This corresponds to treating some rules as optional and reasoning about which conclusions remain valid regardless of the inclusion of these optional rules. While a version of possibilistic ASP (PASP) based on this view has recently been introduced, no implementation is currently available. In this paper we propose a simulation of the main reasoning tasks in PASP using (disjunctive) ASP programs, allowing us to take advantage of state-of-the-art ASP solvers. Furthermore, we identify how several interesting AI problems can be naturally seen as special cases of the considered reasoning tasks, including cautious abductive reasoning and conformant planning. As such, the proposed simulation enables us to solve instances of the latter problem types that are more general than what current solvers can handle.

A primer for use of genetic tools in selecting and testing the suitability of set-aside sites protected from deep-sea seafloor massive sulfide mining activities

Seafloor massive sulfide (SMS) mining will likely occur at hydrothermal systems in the near future. Alongside their mineral wealth, SMS deposits also have considerable biological value. Active SMS deposits host endemic hydrothermal vent communities, whilst inactive deposits support communities of deep water corals and other suspension feeders. Mining activities are expected to remove all large organisms and suitable habitat in the immediate area, making vent endemic organisms particularly at risk from habitat loss and localised extinction. As part of environmental management strategies designed to mitigate the effects of mining, areas of seabed need to be protected to preserve biodiversity that is lost at the mine site and to preserve communities that support connectivity among populations of vent animals in the surrounding region. These "set-aside" areas need to be biologically similar to the mine site and be suitably connected, mostly by transport of larvae, to neighbouring sites to ensure exchange of genetic material among remaining populations. Establishing suitable set-asides can be a formidable task for environmental managers, however the application of genetic approaches can aid set-aside identification, suitability assessment and monitoring. There are many genetic tools available, including analysis of mitochondrial DNA (mtDNA) sequences (e.g. COI or other suitable mtDNA genes) and appropriate nuclear DNA markers (e.g. microsatellites, single nucleotide polymorphisms), environmental DNA (eDNA) techniques and microbial metagenomics. When used in concert with traditional biological survey techniques, these tools can help to identify species, assess the genetic connectivity among populations and assess the diversity of communities. How these techniques can be applied to set-aside decision making is discussed and recommendations are made for the genetic characteristics of set-aside sites. A checklist for environmental regulators forms a guide to aid decision making on the suitability of set-aside design and assessment using genetic tools. This non-technical primer document represents the views of participants in the VentBase 2014 workshop.

Towards a spectroscopically accurate set of potentials for heavy hydride laser cooling candidates: effective core potential calculations of BaH

BaH (and its isotopomers) is an attractive molecular candidate for laser cooling to ultracold temperatures and a potential precursor for the production of ultracold gases of hydrogen and deuterium. The theoretical challenge is to simulate the laser cooling cycle as reliably as possible and this paper addresses the generation of a highly accurate ab initio $^{2}\Sigma^+$ potential for such studies. The performance of various basis sets within the multi-reference configuration-interaction (MRCI) approximation with the Davidson correction (MRCI+Q)is tested and taken to the Complete Basis Set (CBS) limit. It is shown that the calculated molecular constants using a 46 electron Effective Core-Potential (ECP) and even-tempered augmented polarized core-valence basis sets (aug-pCV$n$Z-PP, n= 4 and 5) but only including three active electrons in the MRCI calculation are in excellent agreement with the available experimental values. The predicted dissociation energy De for the X$^2\Sigma^+$ state (extrapolated to the CBS limit) is 16895.12 cm$^{-1}$ (2.094 eV), which agrees within 0.1$\%$ of a revised experimental value of <16910.6 cm$^{-1}$, while the calculated re is within 0.03 pm of the experimental result.