Monotonic Reasoning Research Articles

Logic of defeasible permission and its dynamics

Abstract This paper develops a deontic logic for defeasible permission and studies norm change in various updated semantics. When one grants that $\varphi $ or $\psi $ is permitted, normally, it goes together with the conjunction of a permission of $\varphi $ and that of $\psi $. In the monotonic reasoning on this permission, a permission of $\varphi $ leads to a permission of $\varphi $ and $\psi $; however, if a prohibition of $\psi $ is introduced, we get into trouble. We face a paradox of free choice permission. Many solutions have been proposed, but a systematic account of handling norm change is still needed. This paper first introduces the notion of normality to develop a sound and complete deontic logic for defeasible permission, which can be used to analyse several notions in natural language and in game theory. Further, following Lewis’ idea of norm change, a systematic way to capture various dynamics for updating permission and obligation is proposed.

Propositional Constraint Graphs: An Intuitive, Domain-General Tool for Diagramming Knowledge, Assumptions, and Uncertainties

A diagramming method called Propositional Constraint (PC) graphing was developed as an aid for tasks involving argumentation, planning, and design. Motivated by several AI models of defeasible (or non- monotonic) reasoning, PC graphs were designed to represent knowledge according to an analogical framework in which constraints (e.g., evidence, goals, system constraints) may elicit or deny possibilities (e.g., explanations, decisions, behaviors). In cases of underspecification, an absence of constraints yields uncertainty and competition among plausible outcomes. In cases of overspecification, no plausible outcome is yielded until one of the constraints is amended or forfeited. This framework shares features with theoretical models of reasoning and argumentation, but despite its intuitiveness and applicability, we know of no modeling language or graphical aid that explicitly depicts this defeasible constraint structure. We describe the syntax and semantics for PC graphing and then illustrate potential uses for it.

Formalizing common belief with no underlying assumption on individual beliefs

This paper formalizes common belief among players with no underlying assumption on their individual beliefs. Especially, players may not be logically omniscient, i.e., they may not believe logical consequences of their beliefs. The key idea is to use a novel concept of a common basis: it is an event such that, whenever it is true, every player believes its logical consequences. The common belief in an event obtains when a common basis implies the mutual belief in that event. If players' beliefs are assumed to be true, then common belief reduces to common knowledge. The formalization nests previous axiomatizations of common belief and common knowledge which have assumed players' logical monotonic reasoning. Under this formalization, unlike others, if players have common belief in rationality then their actions survive iterated elimination of strictly dominated actions even if their beliefs are not monotonic.

Beyond subgoaling: A dynamic knowledge generation framework for creative problem solving in cognitive architectures

In this paper we propose a computational framework aimed at extending the problem solving capabilities of cognitive artificial agents through the introduction of a novel, goal-directed, dynamic knowledge generation mechanism obtained via a non monotonic reasoning procedure. In particular, the proposed framework relies on the assumption that certain classes of problems cannot be solved by simply learning or injecting new external knowledge in the declarative memory of a cognitive artificial agent but, on the other hand, require a mechanism for the automatic and creative re-framing, or re-formulation, of the available knowledge. We show how such mechanism can be obtained trough a framework of dynamic knowledge generation that is able to tackle the problem of commonsense concept combination. In addition, we show how such a framework can be employed in the field of cognitive architectures in order to overcome situations like the impasse in SOAR by extending the possible options of its subgoaling procedures.

Applications of Linear Defeasible Logic: combining resource consumption and exceptions to energy management and business processes

Linear Logic and Defeasible Logic have been adopted to formalise different features of knowledge representation: consumption of resources, and non monotonic reasoning in particular to represent exceptions. Recently, a framework to combine sub-structural features, corresponding to the consumption of resources, with defeasibility aspects to handle potentially conflicting information, has been discussed in literature, by some of the authors. Two applications emerged that are very relevant: energy management and business process management. We illustrate a set of guide lines to determine how to apply linear defeasible logic to those contexts.

Recalling a witness: foundations and applications of monotonic state

We provide a way to ease the verification of programs whose state evolves monotonically. The main idea is that a property witnessed in a prior state can be soundly recalled in the current state, provided (1) state evolves according to a given preorder, and (2) the property is preserved by this preorder. In many scenarios, such monotonic reasoning yields concise modular proofs, saving the need for explicit program invariants. We distill our approach into the monotonic-state monad , a general yet compact interface for Hoare-style reasoning about monotonic state in a dependently typed language. We prove the soundness of the monotonic-state monad and use it as a unified foundation for reasoning about monotonic state in the F ⋆ verification system. Based on this foundation, we build libraries for various mutable data structures like monotonic references and apply these libraries at scale to the verification of several distributed applications.

Preferences in artificial intelligence

The paper presents a focused survey about the presence and the use of the concept of preferences in Artificial Intelligence. Preferences are a central concept for decision making and have extensively been studied in disciplines such as economy, operational research, decision analysis, psychology and philosophy. However, in the recent years it has also become an important topic both for research and applications in Computer Science and more specifically in Artificial Intelligence, in fields spanning from recommender systems to automatic planning, from non monotonic reasoning to computational social choice and algorithmic decision theory. The survey essentially covers the basics of preference modelling, the use of preference in reasoning and argumentation, the problem of compact representations of preferences, preference learning and the use of non conventional preference models based on extended logical languages. It aims at providing a general reference for all researchers both in Artificial Intelligence and Decision Analysis interested in this exciting interdisciplinary topic.

Be Nice! How Simple Imperatives Simplify Imperative Logic

In a series of articles, P. Vranas recently proposed a new imperative logic. The strong and weak inferences of this logic are motivated by an appeal to a strong and weak ‘support by reasons’ that transfers from the premisses of an argument to its conclusion. They also combine nonmonotonic and monotonic reasoning patterns. I show that for any moral agent, Vranas’s proposal can be simplified enormously.

Introduction to the 27th International Conference on Logic Programming Special Issue

Following the initiative in 2010 taken by the Association for Logic Programming and Cambridge University Press, the full papers accepted for the International Conference on Logic Programming again appear as a special issue of Theory and Practice of Logic Programming (TPLP)—the 27th International Conference on Logic Programming Special Issue. Papers describing original, previously unpublished research and not simultaneously submitted for publication elsewhere were solicited in all areas of logic programming including but not restricted to: Theory: Semantic Foundations, Formalisms, Non- monotonic Reasoning, Knowledge Representation. Implementation: Compilation, Memory Management, Virtual Machines, Parallelism. Environments: Program Analysis, Transformation, Validation, Verification, Debugging, Profiling, Testing. Language Issues: Concurrency, Objects, Coordination, Mobility, Higher Order, Types, Modes, Assertions, Programming Techniques. Related Paradigms: Abductive Logic Programming, Inductive Logic Programming, Constraint Logic Programming, Answer-Set Programming. Applications: Databases, Data Integration and Federation, Software Engineering, Natural Language Processing, Web and Semantic Web, Agents, Artificial Intelligence, Bioinformatics.

Using ASP for knowledge management with user authorization

Unlike conventional rule based knowledge bases (KBs) that support monotonic reasoning, a key correctness issue, i.e. the correctness of a sub-KB with respect to the full KB, arises when using a KB represented by non-monotonic reasoning languages such as Answer Set Programming (ASP). Since a user may have rights to access only a subset of a KB, the non-monotonic nature of ASP may cause the occurrence of consequences, which are erroneous in the sense that the consequences are not reasonable in the full KB. This paper proposes an approach dealing with the problem. The main idea is to let the usage of Closed World Assumptions (CWAs) for literals in a KB satisfy certain constraints. Two kinds of access right propositions are created, rule retrieval right propositions to control the access to rules, and CWA right propositions to control the usage of CWAs for literals. Based on these right propositions, this paper first defines an algorithm for translating an original KB into a KB tagged by right propositions, and then discusses the right dependency in a KB and proposes methods for checking and obtaining a set of rights that is closed under a set of dependency rules. Finally, several results on the correctness of a set of rights in a KB are presented, which serve as guidelines for the correct use of a KB. As an example, a KB of illness-related financial support for teachers of a university is presented to illustrate the application of our approach.

A survey of paraconsistent annotated logics and applications

In this expository paper, we discuss some applications of the paraconsistent annotated logics (PAL). PAL is a 2-sorted logic that can build a programming language allowing manipulated impreciseness, inconsistencies and paracompleteness in its interior. Also, with suitable rules, it is possible to deal with defesiable-deontic reasoning and many monotonic and non-monotonic reasoning. Also, it is useful to obtain logical frameworks for usual modal systems and in this paper we discuss aspects of them, showing the power of these logical systems.

Designing logic-based robots.

A rational agent exploring a complex and dynamic environment with incomplete information needs cognitive capabilities, e.g. planning, in addition to its perception and reaction for basic functionalities. However, mere planning, i.e., reasoning about sequences of actions, is not sufficient to solve problems in such complex environment. This is because (i) agents need to execute actions while they plan, (ii) they must gather and interpret sensor information, (iii) revise their world model, and (iv) adapt their own goals during a task. The knowledge representation and non monotonic reasoning area has shown the advantage of using logical formalisms to specify rational agents for complex robot applications, also called cognitive robotics applications. An example of such formalism is the Golog language and its different dialects. What those areas are still missing is implementational testbeds to evaluate existing theories. Since practical experimentation highlights the need for the improvement of existing formal theories at the ontological level. This work presents a logic-based implementation of an agent for the Wumpus World domain, which can be envisaged as a simplified model of an agent that reasons logically about its actions and sensor information in the presence of incomplete knowledge. Through a complete implementation of an agent in a real robot, the LegoMindStorm robot, we show some experiments to verify that the Wumpus World can be an implementational testbed used to identify difficulties in transforming theory into operational solutions.

Special Issue on Intelligent Technologies, Fuzzy Systems and Applications

In this issue, we are featuring fifteen papers devoted to intelligent technologies, fuzzy systems and their applications as a special issue of the journal. The papers are selected from papers accepted and presented at the joint Third International Conference on Intelligent Technologies and Third Vietnam-Japan Symposium on Fuzzy Systems and Applications (InTech/VJFuzzy'2002) that was held in Hanoi, Vietnam on December 3-5, 2002. In InTech/VJFuzzy'2002, there was a wide spectrum of research topics on artificial intelligence, fuzzy systems, soft computing, and related fields such as"fuzzy logic", "fuzzy set theory", "fuzzy systems", "AI techniques", "Bayesian networks", "genetic algorithms", "neural networks", "knowledge discovery and data mining", "speech recognition", "soft computing in medicine", among others. More than 60 papers were accepted and presented by authors from many countries, including Australia, China, India, Korea, Germany, France, Thailand, Taiwan, Japan, Vietnam, and U.S.A. Fifteen papers that received outstanding recommendations from its reviews were selected in this special issue. The topics addressed by these selected papers include fuzzy rule systems, fuzzy inference methods, fuzzy and rough models, problem solving with equivalent transformation, genetic algorithms, reinforcement learning, non–monotonic reasoning, support vector machines, Hedge algebra, intelligent control, natural language understanding, self–organizing map learning, soft computing and data mining in medicine. As editors of this special issue, we would like to express our sincere gratitude to paper's authors in this issue. Our special thanks go to the anonymous referees for their excellent job, Ms. Kumiko Sato for her help in coordinating the publication of the issue, the Editorial Board of JACIII, especially Professor Kaoru Hirota for his great support and encouragement. Finally, we wish to thank Professors Hung T. Nguyen, Michio Sugeno and Pratit Santiprabhob for their help and contribution to InTech/VJFuzzy'2002. Without their support, the InTech/VJFuzzy'2002 and this issue would not be possible.

HEURISTICS FOR A DEFAULT LOGIC REASONING SYSTEM

In Artificial Intelligence, Default Logic is recognized as a powerful framework for knowledge representation when one has to deal with incomplete information. Its expressive power is suitable for non monotonic reasoning, but the counterpart is its very high level of theoretical complexity. Today, some operational systems are able to deal with real world applications. However, finding a default logic extension in a practical way is not yet possible in whole generality. This paper which is an extended version of18 shows how heuristics such as Genetic Algorithms and Local Search techniques can be used and combined to build an automated default reasoning system. We give a general description of the required basic components and we exhibit experimental results.

Logical inference of clauses based on Petri net models

This paper extends the logical inference of Horn clauses in Petri net models to cover a large class of non-Horn clauses. Based on four-valued logic and the conflict transition concept, we show how the Petri net model for this class of non-Horn clauses can be constructed. The clause inference is solved by the T-invariant method or the fixpoint of markings. Both forward and backward inference can be used in our model. It is further shown that these techniques are efficient for the common classes of monotonic reasoning.

Non monotonic reasoning and belief revision: syntactic, semantic, foundational and coherence approaches

ABSTRACT The major approaches to belief revision and non monotonic reasoning proposed in the literature differ along a number of dimensions, including whether they are “syntax- based” or “semantic-based”, “foundational” or “coherentist”, “consistence-restoring” or “inconsistency-tolerant”. Our contribution towards clarifying the connections between these various approaches is threefold: •We show that the two main approaches to belief revision, the foundations and coherence theories, are mathematically equivalent, thus answering a question left open in [Gar90, Doy92], The distinction between syntax-based approaches to revision and approaches based on (semantic) preferential structures falls along similar lines, and their expressive equivalence is a consequence of this result. •We formally clarify the connection between belief revision and non monotonic reasoning, in a particularly simple way which also throws light on the connection between consistence- restoring and reasoning-from-inconsistency approaches [BDP95]. •As a direct application of the above, we show that Poole's (syntax-based) system of default reasoning and Shoham's preferential semantic for non monotonic reasoning are also expressively equivalent, in that they can represent the same set of non monotonic consequence relations.

A deductive environment for dealing with objects and nonmonotonic reasoning

The Bottom-up Query machine (BQM)-the role played by our system in the framework of the KIWIS system (K. Apt et al., 1987)-extends deductive database technology with knowledge structuring capabilities to provide an advanced environment for the development of data and knowledge based applications. The system relies on a knowledge representation language that combines the declarativeness of logic programming with the notions of object, inheritance with exceptions, and message passing. Exceptions are supported by allowing rules with negated heads. The use of exceptions inside the inheritance mechanism makes the language inherently nonmonotonic. The paper contains a comprehensive description of both the language and the implementation principles of the BQM system. It begins by providing a model theoretic semantics of the language based on the notion of least model. A fixpoint semantics, providing a constructive definition of the least model, is given as well. Then, a number of implementation techniques for efficient query evaluation are described. Such techniques significantly extend "traditional" deductive database query evaluation strategies to deal with monotonic reasoning. A description of the architecture of the current prototype of the BQM system is also given.

A qualitative approach to face uncertainty in decision models

Inaccurate determination, uncertainty, imprecision and ambiguity are often present in complex decision situations where decision aid is requested. Instead of reducing complexity via quantitative models of preferences, as traditional preference modeling does, it may be necessary to represent these situations explicitly. There exist operational methods that face these problems, the principal reference being the partial comparability theory. The lack of an axiomatization however limits the operational potentialities of this theory. In the paper an axiomatic foundation of the partial comparability theory is outlined based on a sound and complete four valued logic (the truth values “true”, “false”, “unknown”, “contradictory” are accepted). This logic is extended to the first order predicate calculus. Four basic preference relations are thus defined, namely: strict preference, weak preference, indifference and incomparability. The operational perspectives are discussed in the paper as some problems in multicriteria methods can be solved in a much easier and natural way. Moreover non monotonic reasoning devices could be built enhancing the potentialities of the theory.

Models for Belief Revision

*The first part of this paper was discussed at the 1990 SOFIA Conference, in Campinas, Brazil. The second part was worked in part with the help of Jonathan Mills, and presented at the 1989 Interamerican Philosophy Congress in Buenos Aires, Argentina. The third part owes a lot to discussions I've had with Michael Dunn, Michael Gasser, Gordon Beavers, and meetings of the Indiana University Philosophy/H&PS ABD Discussion Group. 1We say that a relation 0 monotonic under a function a if 0(a, b) entails O(a(a), c(b)). In the case of monotonic reasoning, 0 the relation is inferred and a any function that adds semantic content. In other words, adding information to the premisses increases the information in the conclusion: a -b = a & c -b & c. Some people prefer the weaker a -b =t a & c -b, taking x & y -y for granted. 2Skyrms (1990). This paper builds on ideas from Skyrms (1984) and Skyrms (1987).

Formalizing default reasoning

Fuzzy set systems can be used to solve the problem with uncertain knowledge, and default logic can be used to solve the problem with incomplete knowledge, in some sense. In this paper, based on interval-valued fuzzy sets we introduce a method of inference which combines approximate reasoning and default logic, and give the procedure of transforming monotonic reasoning into default reasoning.