Given an abstract argumentation framework ({p,q},{(p,q)}) in which an argument p attacks another argument q, argumentation semantics normally concludes that p is accepted and q is rejected. To reject p, on the other hand, a counter-argument attacking p is to be introduced. However, a player participating in an argumentation or a person in the audience of a public debate would have opinions such that “I do not believe p”, “I still believe q”, or “I do not believe that p attacks q” without any concrete grounds. In this study, we introduce the notions of AF with beliefs and belief extensions to represent interaction between arguments and beliefs. Those notions are used for modelling the audience of argumentation, dialogue between two agents, and inner conflict of an agent.

In logic programming, partial evaluation (PE) performs unfolding rules in advance to reduce the cost of inferencing. Recently, PE of logic programs has been implemented in vector spaces by computing the powers of matrix representations. It has been reported that linear algebraic PE substantially enhances the practical performance of linear algebraic methods for logic programming. However, most recent research has focused exclusively on And-rules, assuming that their dependency graph is acyclic. In this paper, we introduce cycle-resolving techniques to ensure that linear algebraic PE works effectively even with cycles in the program. Additionally, we demonstrate that linear algebraic PE can also be extended to accommodate Or-rules. Moreover, we propose using eigendecomposition and Jordan normal form to conduct PE in vector spaces. We compare the proposed techniques on a set of acyclic and cyclic logic programs to evaluate their effectiveness. It is shown that the iteration method for PE, especially with sparse format, is the most efficient one in general cases. However, the decomposition method has the potential for future research to leverage eigenvalues and eigenvectors of program matrices for reasoning.

Abstract Given a conditional sentence “ ${\varphi}\Rightarrow \psi$ " (if ${\varphi}$ then $\psi$ ) and respective facts, four different types of inferences are observed in human reasoning: Affirming the antecedent (AA) (or modus ponens) reasons $\psi$ from ${\varphi}$ ; affirming the consequent (AC) reasons ${\varphi}$ from $\psi$ ; denying the antecedent (DA) reasons $\neg\psi$ from $\neg{\varphi}$ ; and denying the consequent (DC) (or modus tollens) reasons $\neg{\varphi}$ from $\neg\psi$ . Among them, AA and DC are logically valid, while AC and DA are logically invalid and often called logical fallacies. Nevertheless, humans often perform AC or DA as pragmatic inference in daily life. In this paper, we realize AC, DA and DC inferences in answer set programming. Eight different types of completion are introduced, and their semantics are given by answer sets. We investigate formal properties and characterize human reasoning tasks in cognitive psychology. Those completions are also applied to commonsense reasoning in AI.

Predicting air ticket demand is crucial for both airline companies and travel agencies, while the task is generally hard due to its dynamic nature and few attempts have been made to apply machine learning techniques for this purpose. This paper provides an empirical study for predicting airline tickets sales using deep neural networks. A new learning model is introduced by extending the Long Short-Term Memory (LSTM) for handling non-time series data as well as time series data. The proposed model is compared with the SARIMAX model that is used for forecasting time series data with seasonal patterns. We perform experiments using real data and show that the proposed model captures demand changes better than the SARIMAX. In particular, features related to the day of the week and different airlines are well predicted.

Linear algebraic characterization of logic programs has been investigated to perform logical inference in large-scale knowledge bases and has gained encouraging results. In this paper, we further extend the linear algebraic characterization in abductive reasoning by exploiting the transpose of the program matrix. Then we propose an efficient exhaustive search strategy, which combines the flexibility and robustness of numerical computation with the compactness and efficiency of set operations, in order to compute solutions of abductive Horn propositional tasks. Experimental results demonstrate that our method is competitive with conflict-driven techniques and has the potential to speed up on parallel computing platforms.

Abstract In this paper, we introduce methods of encoding propositional logic programs in vector spaces. Interpretations are represented by vectors and programs are represented by matrices. The least model of a definite program is computed by multiplying an interpretation vector and a program matrix. To optimize computation in vector spaces, we provide a method of partial evaluation of programs using linear algebra. Partial evaluation is done by unfolding rules in a program, and it is realized in a vector space by multiplying program matrices. We perform experiments using artificial data and real data, and show that partial evaluation has the potential for realizing efficient computation of huge scale of programs in vector spaces.

The paper introduces the notion of an epistemic argumentation framework (EAF) as a means to integrate the beliefs of a reasoner with argumentation. Intuitively, an EAF encodes the beliefs of an agent who reasons about arguments. Formally, an EAF is a pair of an argumentation framework and an epistemic constraint. The semantics of the EAF is defined by the notion of an ω-epistemic labelling set, where ω is complete, stable, grounded, or preferred, which is a set of ω-labellings that collectively satisfies the epistemic constraint of the EAF. The paper shows how EAF can represent different views of reasoners on the same argumentation framework. It also includes representing preferences in EAF and multi-agent argumentation. Finally, the paper discusses complexity issues and computation using epistemic logic programming.

We propose a new approach to abduction, i.e., non-deductive inference to find a hypothesis H for an observation O such that H,KB |- O where KB is background knowledge. We reformulate it linear algebraically in vector spaces to abduce ``relations'', not logical formulas, to realize approximate but scalable abduction that can deal with web-scale knowledge bases. More specifically we consider the problem of abducing relations for Datalog programs with binary predicates. We treat two cases, the non-recursive case and the recursive case. In the non-recursive case, given r1(X,Y) and r3(X,Z), we abduce r2(Y,Z) so that r3(X,Z) <= r1(X,Y)&r2(Y,Z) approximately holds, by computing a matrix R2 that approximately satisfies a matrix equation R3 = min1(R1R2) containing a nonlinear function min1(x). Here R1, R2 andR3 encode as adjacency matrix r1(X,Y), r2(Y,Z) and r3(Y,Z) respectively. We apply this matrix-based abduction to rule discovery and relation discovery in a knowledge graph. The recursive case is mathematically more involved and computationally more difficult but solvable by deriving a recursive matrix equation and solving it. We illustrate concrete recursive cases including a transitive closure relation.

This paper studies representation of argumentation frameworks (AFs) in answer set programming (ASP). Four different transformations from AFs to logic programs are provided under the complete semantics, stable semantics, grounded semantics and preferred semantics. The proposed transformations encode labelling-based argumentation semantics in a simple manner, and different semantics of AFs are uniformly characterized by stable models of transformed programs. We apply transformed programs to solving AF problems such as query-answering, enforcement of arguments, agreement or equivalence of different AFs. Logic programming encodings of AFs are also used for representing assumption-based argumentation (ABA) in ASP. The results of this paper exploit new connections between argumentation theory and logic programming, and enable one to perform various argumentation tasks using existing answer set solvers.

Delayed effects are important in modeling biological systems, and timed Boolean networks have been proposed for such a framework. Yet it is not an easy task to design such Boolean models with delays precisely. Recently, an attempt to learn timed Boolean networks has been made in Ribeiro et al 2015 in the framework of learning state transition rules from time-series data. However, this approach still has two limitations: (1) The maximum delay has to be given as input to the algorithm, (2) The possible value of each state is assumed to be Boolean, i.e., twovalued. In this paper, we extend the previous learning mechanism to overcome these limitations. We propose an algorithm to learn multi-valued biological models with delayed influence by automatically tuning the delay. The delay is determined so as to minimally explain the necessary influences. The merits of our approach is then verified on benchmarks coming from the DREAM4 challenge.

In a formal argumentation framework, one is interested in whether a particular argument is accepted or not under argumentation semantics. When an argument A is accepted, on the other hand, one may ask a question “what if A were rejected?” We formulate such counterfactual reasoning in abstract argumentation frameworks. Based on Lewis's logic, we define two counterfactual conditionals in AF and investigate formal properties. We also argue counterfactual dependencies in AF and modal interpretation of AF in terms of counterfactual conditionals.

The article introduces a logical framework for negotiation among dishonest agents. The framework relies on the use of abductive logic programming as a knowledge representation language for agents to deal with incomplete information and preferences. The article shows how intentionally false or inaccurate information of agents can be encoded in the agents' knowledge bases. Such disinformation can be effectively used in the process of negotiation to have desired outcomes by agents. The negotiation processes are formulated under the answer set semantics of abductive logic programming, and they enable the exploration of various strategies that agents can employ in their negotiation. A preliminary implementation has been developed using the ASP-Prolog platform.

In this paper we consider a debate game between two players in which a player may provide false or inaccurate arguments as a tactic to win the game. We formulate a debate game using a formal argumentation framework and investigate situation where a player may provide dishonest arguments in the game. We also argue how a player can detect dishonest arguments of the opponent player.

The paper introduces a logical framework for negotiation among dishonest agents. The framework relies on the use of abductive logic programming as a knowledge representation language for agents to deal with incomplete information and preferences. The paper shows how intentionally false or inaccurate information of agents could be encoded in the agents' knowledge bases. Such disinformation can be effectively used in the process of negotiation to have desired outcomes by agents. The negotiation processes are formulated under the answer set semantics of abductive logic programming and enable the exploration of various strategies that agents can employ in their negotiation.

This paper introduces two methods for comparing explanation power of different abductive theories. One is comparing for observations, and the other is comparing explanation content for observations. Those two measures are represented by generality relations over abductive theories. The generality relations are naturally related to the notion of abductive equivalence introduced by Inoue and Sakama. We also analyze the computational complexity of these relations.

This article studies a semantics of multiple logic programs, and synthesizes a program having such a collective semantics. More precisely, the following two problems are considered: given two logic programs P 1 and P 2 , which have the collections of answer sets AS ( P 1 ) and AS ( P 2 ), respectively; (i) find a program Q which has the set of answer sets such that AS ( Q ) = AS ( P 1 ) ∪ AS ( P 2 ); (ii) find a program R which has the set of answer sets such that AS ( R ) = AS ( P 1 ) ∩ AS ( P 2 ). A program Q satisfying the condition (i) is called generous coordination of P 1 and P 2 ; and R satisfying (ii) is called rigorous coordination of P 1 and P 2 . Generous coordination retains all of the answer sets of each program, but permits the introduction of additional answer sets of the other program. By contrast, rigorous coordination forces each program to give up some answer sets, but the result remains within the original answer sets for each program. Coordination provides a program that reflects the meaning of two or more programs. We provide methods for constructing these two types of coordination and address its application to logic-based multi-agent systems.

Inductive logic programming (ILP) realizes inductive machine learning in computational logic. However, the present ILP mostly handles classical clausal programs, especially Horn logic programs, and has limited applications to learning nonmonotonic logic programs . This article studies a method for realizing induction in nonmonotonic logic programs. We consider an extended logic program as a background theory, and introduce techniques for inducing new rules using answer sets of the program. The produced new rules explain positive/negative examples in the context of inductive logic programming. The proposed methods extend the present ILP techniques to a syntactically and semantically richer framework, and contribute to a theory of nonmonotonic ILP.

This paper introduces an abductive framework for updating knowledge bases represented by extended disjunctive programs. We first provide a simple transformation from abductive programs to update programs which are logic programs specifying changes on abductive hypotheses. Then, extended abduction, which was introduced by the same authors as a generalization of traditional abduction, is computed by the answer sets of update programs. Next, different types of updates, view updates and theory updates are characterized by abductive programs and computed by update programs. The task of consistency restoration is also realized as special cases of these updates. Each update problem is comparatively assessed from the computational complexity viewpoint. The result of this paper provides a uniform framework for different types of knowledge base updates, and each update is computed using existing procedures of logic programming.

This paper presents declarative semantics of possibly inconsistent disjunctive logic programs. We introduce the paraconsistent minimal and stable model semantics for extended disjunctive programs, which can distinguish inconsistent information from other information in a program. These semantics are based on lattice-structured multi-valued logics, and are characterized by a new fixpoint semantics of extended disjunctive programs. Applications of the paraconsistent semantics for reasoning in inconsistent programs are also presented.

We assume a back-end type relational data base machine equipped with multiple dedicated engines for relational database operations. Response characteristics are evaluated, and some parallel control techniques are considered for improved response time by simulating the database machine in executing relational database operations using these engines in parallel.