The Bdi model of rational agency has been studied for over three decades. Many robust multiagent systems have been developed, and a number of Bdi logics have been studied. Following this intensive development phase, the importance of integrating Bdi models with inconsistency handling and revision theory have been emphasized. There is also a demand for a tighter connection between Bdi-based implementations and Bdi logics. In this paper, we address these postulates by introducing a novel, paraconsistent logical Bdi model close to implementation, with building blocks that can be represented as Sql/rule-based databases. Importantly, tractability is achieved by reasoning as querying. This stands in a sharp contrast to the high complexity of known Bdi logics. We also extend belief shadowing, a shallow and lightweight alternative to deep and computationally demanding belief revision, to encompass agents motivational attitudes.

Inheritance has intensively been studied in both object-oriented programming (Oop) and knowledge representation and reasoning (KRR). On the other hand, the approaches to multiple inheritance and related method resolution, developed in both domains, remain separated. The primary goal of this paper is to demonstrate how these approaches may be integrated using inheritance expressions. In particular, we examine inheritance as a belief bases management machinery designed to operate in dynamically changing environments where objects are embedded and act. We focus on objects that are belief bases containers, potentially participating in complex distributed reasoning scenarios. We show that inheritance expressions, inspired both by Oop and KRR, provide a simple yet flexible and powerful means for expressing inheritance and related belief/knowledge fusion.

For over three decades researchers have been studying the BDI modelof agency. Many robust multiagent systems have been developed, and a numberof BDI logics have been studied. Following this intensive development phase, theimportance of integrating BDI models with inconsistency handling and revisiontheory have been emphasized. There is also a demand for a tighter connectionbetween BDI-based implementations and BDI logics. In this paper, we addressthese postulates by introducing a novel, paraconsistent logical BDI model close toimplementation, with building blocks that can be represented as SQL/rule-baseddatabases. Importantly, tractability is achieved by reasoning as querying. Thisstands in a sharp contrast to the high complexity of BDI logics. We also extendbelief shadowing, a shallow and lightweight alternative to deep and computation-ally demanding belief revision, to encompass agents’ motivational attitudes.

Inheritance has intensively been investigated during the past decades in object-oriented programming and knowledge representation and reasoning areas. In the paper we focus on recently introduced inheritance expressions that allow one to represent dynamic concept hierarchies as well as fuse and disambiguate beliefs acquired by the objects involved. We focus on querying and reasoning about inheritance expressions using a four-valued paraconsistent formalism that has been developed over the last ten years. In particular, we show that querying inheritance expressions and formulas can be efficiently implemented. In addition, we provide tableaux for general reasoning purposes. Complexity of the investigated tools is also analyzed.

The majority of contemporary software systems are developed using object-oriented tools and methodologies, where constructs like classes, inheritance and objects are first-class citizens. In the current paper we provide a novel formal framework for many-valued object-oriented inheritance in rule-based query languages. We also relate the framework to rough set-like approximate reasoning. Rough sets and their generalizations have intensively been studied and applied. However, the mainstream of the area mainly focuses on the context of information and decision tables. Therefore, approximations defined in the much richer object-oriented contexts generalize known approaches. 

As a side-effect of the Covid-19 pandemic, significant decreases in medical procedures for noncommunicable diseases have been observed. This calls for a decision support assisting in the analysis of opportunities to relocate procedures among hospitals in an efficient or, preferably, optimal manner. In the current paper we formulate corresponding decision problems and develop linear (mixed integer) programming models for them. Since solving mixed integer programming problems is NP-complete, we verify experimentally their usefulness using real-world data about urological procedures. We show that even for large models, with millions of variables, the problems’ instances are solved in perfectly acceptable time.

Reasoning about uncertainty is one of the main cornerstones of Knowledge Representation. Formal representations of uncertainty are numerous and highly varied due to different types of uncertainty intended to be modeled such as vagueness, imprecision and incompleteness. There is a rich body of theoretical results that has been generated for many of these approaches. It is often the case though, that pragmatic tools for reasoning with uncertainty lag behind this rich body of theoretical results. Rough set theory is one such approach for modeling incompleteness and imprecision based on indiscernibility and its generalizations. In this paper, we provide a pragmatic tool for constructively reasoning with generalized rough set approximations that is based on the use of Answer Set Programming (Asp). We provide an interpretation of answer sets as (generalized) approximations of crisp sets (when possible) and show how to use Asp solvers as a tool for reasoning about (generalized) rough set approximations situated in realistic knowledge bases. The paper includes generic Asp templates for doing this and also provides a case study showing how these techniques can be used to generate reducts for incomplete information systems. Complete, ready to run clingo Asp code is provided in the Appendix, for all programs considered. These can be executed for validation purposes in the clingo Asp solver.

Answer Set Programming (ASP) is nowadays a dominant rule-based knowledge representation tool. Though existing ASP variants enjoy efficient implementations, generating an answer set remains intractable. The goal of this research is to define a new ASP-like rule language, 4SP, with tractable model generation. The language combines ideas of ASP and a paraconsistent rule language 4QL. Though 4SP shares the syntax of ASP and for each program all its answer sets are among 4SP models, the new language differs from ASP in its logical foundations, the intended methodology of its use and complexity of computing models. As we show in the paper, 4QL can be seen as a paraconsistent counterpart of ASP programs stratified with respect to default negation. Although model generation for 4QL programs is tractable, dropping stratification makes it intractable for both 4QL and ASP. To retain tractability while allowing non-stratified programs, in 4SP we introduce trial expressions interlacing programs with hypotheses as to the truth values of default negations. This allows us to develop a model generation algorithm with deterministic polynomial time complexity. We also show relationships among 4SP, ASP and 4QL.

Ignorance, inconsistency, nonsense and similar phenomena are omnipresent in everyday reasoning. They have been intensively studied, especially in the area of multiple-valued logics. Therefore we develop a framework for belief bases, combining multiple-valued and probabilistic reasoning, with the main focus on the way belief bases are actually used and accessed through queries.

As an implementation tool we use a probabilistic programming language PROBLOG. Though based on distribution semantics with the independence assumption, we show how its constructs can successfully be used in implementing the considered logics and belief bases. In particular, we develop a technique for shifting probabilistic dependencies to the level of symbolic parts of belief bases.

We also discuss applications of the framework in reasoning with Likert-type scales, widely exploited in questionnaire-based experimental research in psychology, economics, sociology, politics, public opinion measurements, and related areas.