We describe a compilation language of backdoor decomposable monotone circuits (BDMCs) which generalizes several concepts appearing in the literature, e.g. DNNFs and backdoor trees. A BDMC sentence is a monotone circuit which satisfies decomposability property (such as in DNNF) in which the inputs (or leaves) are associated with CNF encodings of some functions. We consider two versions of BDMCs. In case of PC-BDMCs the encodings in the leaves are propagation complete encodings and in case of URC-BDMCs the encodings in the leaves are unit refutation complete encodings of respective functions. We show that a representation of a boolean function with a PC-BDMC can be transformed into a propagation complete encoding of the same function whose size is polynomial in the size of the input PC-BDMC sentence. We obtain a similar result in case of URC-BDMCs. We also relate the size of PC-BDMCs to the size of DNNFs and backdoor trees.

In one perspective, the main theme of this research revolves around the inverse problem in the context of general rough sets that concerns the existence of rough basis for given approximations in a context. Granular operator spaces and variants were recently introduced by the present author as an optimal framework for anti-chain based algebraic semantics of general rough sets and the inverse problem. In the framework, various sub-types of crisp and non-crisp objects are identifiable that may be missed in more restrictive formalism. This is also because in the latter cases concepts of complementation and negation are taken for granted - while in reality they have a complicated dialectical basis. This motivates a general approach to dialectical rough sets building on previous work of the present author and figures of opposition. In this paper dialectical rough logics are invented from a semantic perspective, a concept of dialectical predicates is formalised, connection with dialetheias and glutty negation are established, parthood analyzed and studied from the viewpoint of classical and dialectical figures of opposition by the present author. Her methods become more geometrical and encompass parthood as a primary relation (as opposed to roughly equivalent objects) for algebraic semantics.

In logic-based approaches to reasoning tasks such as Recognizing Textual Entailment (RTE), it is important for a system to have a large amount of knowledge data. However, there is a tradeoff between adding more knowledge data for improved RTE performance and maintaining an efficient RTE system, as such a big database is problematic in terms of the memory usage and computational complexity. In this work, we show the processing time of a state-of-the-art logic-based RTE system can be significantly reduced by replacing its search-based axiom injection (abduction) mechanism by that based on Knowledge Base Completion (KBC). We integrate this mechanism in a Coq plugin that provides a proof automation tactic for natural language inference. Additionally, we show empirically that adding new knowledge data contributes to better RTE performance while not harming the processing speed in this framework.

In this machine learning tutorial, we are going to discuss the detailed what is Machine Learning and the difference between data mining and machine learning. Moreover, we will discuss different types of Machine Learning and different approaches to Machine Learning. Machine Learning is a science to make the machine capable of taking the decision itself. These systems also have the ability to learn from past experience or analyze historical data. It provides results according to its experience. So, let's start the Machine Learning Tutorial.

This paper compares classical copying and quantum entanglement in natural language by considering the case of verb phrase (VP) ellipsis. VP ellipsis is a non-linear linguistic phenomenon that requires the reuse of resources, making it the ideal test case for a comparative study of different copying behaviours in compositional models of natural language. Following the line of research in compositional distributional semantics set out by (Coecke et al., 2010) we develop an extension of the Lambek calculus which admits a controlled form of contraction to deal with the copying of linguistic resources. We then develop two different compositional models of distributional meaning for this calculus. In the first model, we follow the categorical approach of (Coecke et al., 2013) in which a functorial passage sends the proofs of the grammar to linear maps on vector spaces and we use Frobenius algebras to allow for copying. In the second case, we follow the more traditional approach that one finds in categorial grammars, whereby an intermediate step interprets proofs as non-linear lambda terms, using multiple variable occurrences that model classical copying. As a case study, we apply the models to derive different readings of ambiguous elliptical phrases and compare the analyses that each model provides.

Answer-set programming (ASP), a family of SAT-based logic programming systems, is attractive for procedural content generation. Unfortunately, current solvers present significant barriers to runtime use in games. In this paper, I discuss some of the issues involved, and present CatSAT, a solver designed to better fit the run-time resource constraints of modern games. Although intended only for small problems, it allows designers to compactly specify simple PCG problems such as NPC generation, solve them in a few tens of microseconds, and to adapt solutions dynamically based on the changing needs of gameplay. We hope that by making adoption as convenient as possible, we can increase the uptake of declarative techniques among developers.

We propose a nonmonotonic Description Logic of typicality able to account for the phenomenon of concept combination of prototypical concepts. The proposed logic relies on the logic of typicality ALC TR, whose semantics is based on the notion of rational closure, as well as on the distributed semantics of probabilistic Description Logics, and is equipped with a cognitive heuristic used by humans for concept composition. We first extend the logic of typicality ALC TR by typicality inclusions whose intuitive meaning is that "there is probability p about the fact that typical Cs are Ds". As in the distributed semantics, we define different scenarios containing only some typicality inclusions, each one having a suitable probability. We then focus on those scenarios whose probabilities belong to a given and fixed range, and we exploit such scenarios in order to ascribe typical properties to a concept C obtained as the combination of two prototypical concepts. We also show that reasoning in the proposed Description Logic is EXPTIME-complete as for the underlying ALC.

Answer set programming (ASP) is a successful declarative formalism for knowledge representation and reasoning. The evaluation of ASP programs is nowadays based on the Conflict-Driven Clause Learning (CDCL) backtracking search algorithm. Recent work suggested that the performance of CDCL-based implementations can be considerably improved on specific benchmarks by extending their solving capabilities with custom heuristics and propagators. However, embedding such algorithms into existing systems requires expert knowledge of the internals of ASP implementations. The development of effective solver extensions can be made easier by providing suitable programming interfaces. In this paper, we present the interface for extending the CDCL-based ASP solver WASP. The interface is both general, i.e. it can be used for providing either new branching heuristics and propagators, and external, i.e. the implementation of new algorithms requires no internal modifications of WASP. Moreover, we review the applications of the interface witnessing it can be successfully used to extend WASP for solving effectively hard instances of both real-world and synthetic problems. Under consideration in Theory and Practice of Logic Programming (TPLP).

Blameworthiness of an agent or a coalition of agents is often defined in terms of the principle of alternative possibilities: for the coalition to be responsible for an outcome, the outcome must take place and the coalition should have had a strategy to prevent it. In this paper we argue that in the settings with imperfect information, not only should the coalition have had a strategy, but it also should have known that it had a strategy, and it should have known what the strategy was. The main technical result of the paper is a sound and complete bimodal logic that describes the interplay between knowledge and blameworthiness in strategic games with imperfect information.

The problem-solving in automated theorem proving (ATP) can be interpreted as a search problem where the prover constructs a proof tree step by step. In this paper, we propose a deep reinforcement learning algorithm for proof search in intuitionistic propositional logic. The most significant challenge in the application of deep learning to the ATP is the absence of large, public theorem database. We, however, overcame this issue by applying a novel data augmentation procedure at each iteration of the reinforcement learning. We also improve the efficiency of the algorithm by representing the syntactic structure of formulas by a novel compact graph representation. Using the large volume of augmented data, we train highly accurate graph neural networks that approximate the value function for the set of the syntactic structures of formulas. Our method is also cost-efficient in terms of computational time. We will show that our prover outperforms Coq's $\texttt{tauto}$ tactic, a prover based on human-engineered heuristics. Within the specified time limit, our prover solved 84% of the theorems in a benchmark library, while $\texttt{tauto}$ was able to solve only 52%.