KR languages based on logic have repeatedly proven their usefulness, e.g. Horn clauses, ASP, or FO logic. As the demand for more powerful and rich KR languages grows, we propose a KR language based on Second-Order (SO) Logic. As SO Logic is more expressive than SAT or ground (disjunctive) ASP, we propose Quantified Boolean Formulas (QBF) as a target language for our specifications. In this paper, we describe SOGrounder, a system that can ground SO Logic specifications to QBF. We start with a basic approach and suggest further techniques for reducing grounding, for example by introducing Binary Quantification as a language construct that takes two formules: One formula generating variable instantiations and one formula that must be instantiated. Finally, we show how to model a real world problem that is not reducible to first-order, and evaluate the performance of SOGrounder w.r.t. grounding time, grounding size and solving time as compared to existing encodings.
In this paper we describe a new quantification theory based on the Object Determination Logic(ODL). This theory extends the system of classical quantifiers as a system including the classical and linguistic ones. It takes into account typicality, as a dimension of cognition. This theory represents the background of a computational model in the semantic analysis of natural languages. This paper presents the basic elements of this quantification system (QSODL) and the possibilities of implementing it in a computational system. Keywords: more or less determined object, concept, typicality, quantifier.
Artificial Intelligence (AI) has become an integral part of domains such as security, finance, healthcare, medicine, and criminal justice. Explaining the decisions of AI systems in human terms is a key challenge--due to the high complexity of the model, as well as the potential implications on human interests, rights, and lives . While Explainable AI is an emerging field of research, there is no consensus on the definition, quantification, and formalization of explainability. In fact, the quantification of explainability is an open challenge. In our previous work, we incorporated domain knowledge for better explainability, however, we were unable to quantify the extent of explainability. In this work, we (1) briefly analyze the definitions of explainability from the perspective of different disciplines (e.g., psychology, social science), properties of explanation, explanation methods, and human-friendly explanations; and (2) propose and formulate an approach to quantify the extent of explainability. Our experimental result suggests a reasonable and model-agnostic way to quantify explainability
High-throughput mRNA sequencing (RNA-Seq) is widely used for transcript quantification of gene isoforms. Since RNA-Seq data alone is often not sufficient to accurately identify the read origins from the isoforms for quantification, we propose to explore protein domain-domain interactions as prior knowledge for integrative analysis with RNA-seq data. We introduce a Network-based method for RNA-Seq-based Transcript Quantification (Net-RSTQ) to integrate protein domain-domain interaction network with short read alignments for transcript abundance estimation. Based on our observation that the abundances of the neighboring isoforms by domain-domain interactions in the network are positively correlated, Net-RSTQ models the expression of the neighboring transcripts as Dirichlet priors on the likelihood of the observed read alignments against the transcripts in one gene. The transcript abundances of all the genes are then jointly estimated with alternating optimization of multiple EM problems. In simulation Net-RSTQ effectively improved isoform transcript quantifications when isoform co-expressions correlate with their interactions. qRT-PCR results on 25 multi-isoform genes in a stem cell line, an ovarian cancer cell line, and a breast cancer cell line also showed that Net-RSTQ estimated more consistent isoform proportions with RNA-Seq data. In the experiments on the RNA-Seq data in The Cancer Genome Atlas (TCGA), the transcript abundances estimated by Net-RSTQ are more informative for patient sample classification of ovarian cancer, breast cancer and lung cancer. All experimental results collectively support that Net-RSTQ is a promising approach for isoform quantification.
We investigate the complexity of satisfiability for one-agent refinement modal logic (RML), an extension of basic modal logic (ML) obtained by adding refinement quantifiers on structures. RML is known to have the same expressiveness as ML, but the translation of RML into ML is of non-elementary complexity, and RML is at least doubly exponentially more succinct than ML. In this paper we show that RML-satisfiability is `only' singly exponentially harder than ML-satisfiability, the latter being a well-known PSPACE-complete problem.