Contradiction-tolerant process algebra with propositional signals

In a previous paper, an ACP-style process algebra was proposed in which propositions are used as the visible part of the state of processes and as state conditions under which processes may proceed. This process algebra, called ACPps, is built on classical propositional logic. In this paper, we present a version of ACPps built on a paraconsistent propositional logic which is essentially the same as CLuNs. There are many systems that would have to deal with self-contradictory states if no special measures were taken. For a number of these systems, it is conceivable that accepting self-contradictory states and dealing with them in a way based on a paraconsistent logic is an alternative to taking special measures. The presented version of ACPps can be suited for the description and analysis of systems that deal with self-contradictory states in a way based on the above-mentioned paraconsistent logic.Comment: 25 pages; 26 pages, occurrences of wrong symbol for bisimulation equivalence replaced; 26 pages, Proposition 1 added; 27 pages, explanation of the phrase 'in contradiction' added to section 2 and presentation of the completeness result in section 2 improved; 27 pages, uniqueness result in section 2 revised; 27 pages, last paragraph of section 8 revise

Efficient paraconsistent reasoning with rules and ontologies for the semantic web

Ontologies formalized by means of Description Logics (DLs) and rules in the form of Logic Programs (LPs) are two prominent formalisms in the field of Knowledge Representation and Reasoning. While DLs adhere to the OpenWorld Assumption and are suited for taxonomic reasoning, LPs implement reasoning under the Closed World Assumption, so that default knowledge can be expressed. However, for many applications it is useful to have a means that allows reasoning over an open domain and expressing rules with exceptions at the same time. Hybrid MKNF knowledge bases make such a means available by formalizing DLs and LPs in a common logic, the Logic of Minimal Knowledge and Negation as Failure (MKNF). Since rules and ontologies are used in open environments such as the Semantic Web, inconsistencies cannot always be avoided. This poses a problem due to the Principle of Explosion, which holds in classical logics. Paraconsistent Logics offer a solution to this issue by assigning meaningful models even to contradictory sets of formulas. Consequently, paraconsistent semantics for DLs and LPs have been investigated intensively. Our goal is to apply the paraconsistent approach to the combination of DLs and LPs in hybrid MKNF knowledge bases. In this thesis, a new six-valued semantics for hybrid MKNF knowledge bases is introduced, extending the three-valued approach by Knorr et al., which is based on the wellfounded semantics for logic programs. Additionally, a procedural way of computing paraconsistent well-founded models for hybrid MKNF knowledge bases by means of an alternating fixpoint construction is presented and it is proven that the algorithm is sound and complete w.r.t. the model-theoretic characterization of the semantics. Moreover, it is shown that the new semantics is faithful w.r.t. well-studied paraconsistent semantics for DLs and LPs, respectively, and maintains the efficiency of the approach it extends

Logic, self-awareness and self-improvement: The metacognitive loop and the problem of brittleness

This essay describes a general approach to building perturbation-tolerant autonomous systems, based on the conviction that artificial agents should be able notice when something is amiss, assess the anomaly, and guide a solution into place. We call this basic strategy of self-guided learning the metacognitive loop; it involves the system monitoring, reasoning about, and, when necessary, altering its own decision-making components. In this essay, we (a) argue that equipping agents with a metacognitive loop can help to overcome the brittleness problem, (b) detail the metacognitive loop and its relation to our ongoing work on time-sensitive commonsense reasoning, (c) describe specific, implemented systems whose perturbation tolerance was improved by adding a metacognitive loop, and (d) outline both short-term and long-term research agendas

Revision based total semantics for extended normal logic programs

Dissertação para obtenção do Grau de Doutor em Matemática - Lógica e Fundamentos da MatemáticaFundação para a Ciência e Tecnologia - SFRH/ PROTEC/49747/200

Revision based total semantics for extended normal logic programs

The purpose of this thesis is the development of a formal semantical approach for extended normal logic programs, where contradictions are tackled by means of a reduction ad absurdum with respect to default negation mechanism, in the fashion of arti cial intelligence belief revision, that leads to a set of implicit revisions. We ful lled these objectives in two steps. The rst one was the implementation of a total paraconsistent models semantics for extended normal logic programs MHP , that combines the merits of two already existing semantics: it inherits the existence property of the abductive minimal hypotheses semantics MH, a semantics of total models, and the property of detection of support on contradiction of the paraconsistent well-founded semantics with explicit negation WFSXP , a semantics of partial paraconsistent models. As for the second step, we developed a revision procedure for inconsistent constrained theories, that tackles inconsistencies arising from contradictions with respect to explicit negation, i.e., L and :L in the same model, and stepping beyond, also tackles inconsistencies arising in more general constrained theories (i.e., theories containing constraints of the type ? A; not B, where A is a conjunction of objective literals and not B stands for a conjunction of default literals). An algorithm for inconsistency propagation detection was also developed. A characterization of the MHP with respect to the semantic formal properties of relevance and cumulativity is furnished, by resorting to a set of results that arose from a detailed study of these properties for a class of 2-valued conservative extensions of the stable models semantics.O objetivo desta tese é o desenvolvimento de uma abordagem formal semântica para programas lógicos normais estendidos (i.e., programas com dois tipos de negação: uma negação explícita e a negação por omissão), na qual as contradições são resolvidas por meio de um mecanismo de raciocínio por redução ao absurdo, ao estilo da revisão de crenças na intelig ência arti cial. Este objectivo foi alcançado em duas etapas. A primeira delas foi a implementação de uma semântica de modelos totais para programas lógicos estendidos, MHP , que combina os méritos de duas semânticas já existentes: herda a propriedade de existência da semântica abdutiva de hipóteses mínimas MH, uma semântica de modelos totais para programas normais; herda também a propriedade de detecção de suporte em contradição da semântica paraconsistente WFSXP , uma semântica de modelos paraconsistentes parciais para programas lógicos estendidos. A segunda etapa consistiu no desenvolvimento de um algoritmo de revisão de teorias inconsistentes, que aborda não apenas inconsistências decorrentes de contradições com respeito à negação explícita, ou seja L e :L no mesmo modelo, mas também inconsistências com respeito a teorias contendo restrições de integridade mais gerais, do tipo ? A; not B, sendo A uma conjunção de literais objectivos e not B uma conjunção de literais objectivos negados por omissão. Um algoritmo de detecção de propagação de inconsistências foi também desenvolvido. É apresentada uma caracterização detalhada da MHP com respeito às propriedades semânticas formais de relevância e cumulatividade, utilizando um conjunto de resultados obtidos de um estudo dessas propriedades para uma classe de extensões conservativas 2-valoradas da semântica de modelos estáveis

Paraconsistency and Plausible Argumentation in Generative Grammar: A Case Study

While the analytical philosophy of science regards inconsistent theories as disastrous, Chomsky allows for the temporary tolerance of inconsistency between the hypotheses and the data. However, in linguistics there seem to be several types of inconsistency. The present paper aims at the development of a novel metatheoretical framework which provides tools for the representation and evaluation of inconsistencies in linguistic theories. The metatheoretical model relies on a system of paraconsistent logic and distinguishes between strong and weak inconsistency. Strong inconsistency is destructive in that it leads to logical chaos. In contrast, weak inconsistency may be constructive, because it is capable of accounting for the simultaneous presence of seemingly incompatible structures. However, paraconsistent logic cannot grasp the dynamism of the emergence and resolution of weak inconsistencies. Therefore, the metatheoretical approach is extended to plausible argumentation. The workability of this metatheoretical model is tested with the help of a detailed case study on an analysis of discontinuous constituents in Government-Binding Theory. Keywords: generative syntax, inconsistency, paraconsistency, plausible argumentatio

Stone-type representations and dualities for varieties of bisemilattices

In this article we will focus our attention on the variety of distributive bisemilattices and some linguistic expansions thereof: bounded, De Morgan, and involutive bisemilattices. After extending Balbes' representation theorem to bounded, De Morgan, and involutive bisemilattices, we make use of Hartonas-Dunn duality and introduce the categories of 2spaces and 2spaces$^{\star}$. The categories of 2spaces and 2spaces$^{\star}$ will play with respect to the categories of distributive bisemilattices and De Morgan bisemilattices, respectively, a role analogous to the category of Stone spaces with respect to the category of Boolean algebras. Actually, the aim of this work is to show that these categories are, in fact, dually equivalent

Modular Logic Programming: Full Compositionality and Conflict Handling for Practical Reasoning

With the recent development of a new ubiquitous nature of data and the profusity of available knowledge, there is nowadays the need to reason from multiple sources of often incomplete and uncertain knowledge. Our goal was to provide a way to combine declarative knowledge bases – represented as logic programming modules under the answer set semantics – as well as the individual results one already inferred from them, without having to recalculate the results for their composition and without having to explicitly know the original logic programming encodings that produced such results. This posed us many challenges such as how to deal with fundamental problems of modular frameworks for logic programming, namely how to define a general compositional semantics that allows us to compose unrestricted modules. Building upon existing logic programming approaches, we devised a framework capable of composing generic logic programming modules while preserving the crucial property of compositionality, which informally means that the combination of models of individual modules are the models of the union of modules. We are also still able to reason in the presence of knowledge containing incoherencies, which is informally characterised by a logic program that does not have an answer set due to cyclic dependencies of an atom from its default negation. In this thesis we also discuss how the same approach can be extended to deal with probabilistic knowledge in a modular and compositional way. We depart from the Modular Logic Programming approach in Oikarinen & Janhunen (2008); Janhunen et al. (2009) which achieved a restricted form of compositionality of answer set programming modules. We aim at generalising this framework of modular logic programming and start by lifting restrictive conditions that were originally imposed, and use alternative ways of combining these (so called by us) Generalised Modular Logic Programs. We then deal with conflicts arising in generalised modular logic programming and provide modular justifications and debugging for the generalised modular logic programming setting, where justification models answer the question: Why is a given interpretation indeed an Answer Set? and Debugging models answer the question: Why is a given interpretation not an Answer Set? In summary, our research deals with the problematic of formally devising a generic modular logic programming framework, providing: operators for combining arbitrary modular logic programs together with a compositional semantics; We characterise conflicts that occur when composing access control policies, which are generalisable to our context of generalised modular logic programming, and ways of dealing with them syntactically: provided a unification for justification and debugging of logic programs; and semantically: provide a new semantics capable of dealing with incoherences. We also provide an extension of modular logic programming to a probabilistic setting. These goals are already covered with published work. A prototypical tool implementing the unification of justifications and debugging is available for download from http://cptkirk.sourceforge.net

Distributed knowledge bases : A proposal for argumentation-based semantics with cooperation

O objectivo principal desta dissertação é definir um ambiente de negociação, baseada em argumentação, para bases de conhecimento distribuídas. As bases de conhecimentos são modeladas sobre um ambiente multiagente tal que cada agente possui uma base de conhecimento própria. As bases de conhecimento dos diversos agentes podem ser independentes ou podem incluir conhecimentos comuns. O requisito mínimo para haver negociação num ambiente multiagente é que os agentes tenham a capacidade de fazer propostas, que poderão ser aceites ou rejeitadas. Numa abordagem mais sofisticada, os agentes poderão responder com contra-propostas, com o intuito de alterar aspectos insatisfatórios da pro­ posta original. Um tipo ainda mais elaborado de negociação será o baseado em argumentação. A metáfora da argumentação parece ser adequada à modelação de situações em que os diferentes agentes interagem com o propósito de determinar o significado das crenças comuns. Numa negociação baseada em argumentação, as (contra­) propostas de um agente podem ser acompanhadas de argumentos a favor da sua aceitação. Um agente poderá, então, ter um argumento aceitável para uma sua crença, se conseguir argumentar com sucesso contra os argumentos, dos outros agentes, que o atacam. Assim, as crenças de um agente caracterizam-se pela relação entre os argumentos "internos" que sustentam suas crenças, e os argumentos "externos" que sustentam crenças contraditórias de outros agentes. Portanto, o raciocínio argumentativo baseia-se na "estabilidade externa" dos argumentos aceitáveis do conjunto de agentes. Neste trabalho propõe-se uma negociação baseada em argumentação em que, para chegarem a um consenso quanto ao conhecimento comum, os agentes constroem argumentos que sustentam as suas crenças ou que se opõem aos argumentos dos agentes que as contradizem. Além disso, esta proposta lida com conhecimento incompleto (i.e., argumentos parciais) pela definição de um processo de cooperação que permite completar tal conhecimento. Assim, a negociação entre agentes é um processo argumentativo-cooperativo, em que se podem alternar os argumentos contra e a favor das crenças de um agente. Para a formação das suas crenças, a cada agente Ag está associado um conjunto Cooperate de agentes com quem coopera e um outro Argue de agentes contra quem argumenta. A negociação proposta permite a modelação de bases de conhecimento hierárquicas, representando, por exemplo, a estrutura de uma organização ou uma taxonomia nalgum domínio, e de ambientes multi-agente em que cada agente representa o conhecimento referente a um determinado período de tempo. Um agente também pode ser inquirido sobre a verdade de uma crença, dependendo a resposta do agente em questão e de quais os agentes que com ele cooperam e que a ele se opõem. Essa resposta será, no entanto, sempre consistente/ paraconsistente com as bases de conhecimento dos agentes envolvidos. Esta dissertação propõe semânticas (declarativa e operacional) da argumentação numa base de conhecimento de um agente. Partindo destas, propõe, também, semântica declarativa da negociação baseada em argumentação num ambiente multi-agente. ⓿⓿⓿ ABSTRACT: The main objective of this dissertation is to define an argumentation-based negotiation framework for distributed knowledge bases. Knowledge bases are modelling over a multi-agent setting such that each agent possibly has an independent or overlapping knowledge base. The minimum requirement for a multi-agent setting negotiation is that agents should be able to make proposals which can then either be accepted or rejected. A higher level of sophistication occurs when recipients do not just have the choice of accepting or rejecting proposals, but have the option of making counter offers to alter aspects of the proposal which are unsatisfactory. An even more elaborate kind of negotiation is argumentation-based. The argumentation metaphor seems to be adequate for modelling situations where different agents argue in order to determine the meaning of common beliefs. ln an argumentation-based negotiation, the agents are able to send justifications or arguments along with (counter) proposals indicating why they should be accepted. An argument for an agent's belief is acceptable if the agent can argue successfully against attacking arguments from other agents. Thus, agent's beliefs are characterized by the relation between its "internal" arguments supporting its beliefs and the "external" arguments supporting the contradictory beliefs of other agents. So, in a certain sense, argumentative reasoning is based on the "external stability" of acceptable arguments in the multi-agent setting. This dissertation proposes that agents evaluate arguments to obtain a consensus about a common knowledge by both proposing arguments or trying to build opposing arguments against them. Moreover, this proposal deals with incomplete knowledge (i.e. partial arguments) and so a cooperation process grants arguments to achieve knowledge completeness. Therefore, a negotiation of an agent's belief is seen as an argumentation-based process with cooperation; both cooperation and argumentation are seen as interlaced processes. Furthermore, each agent Ag has both set Argue of argumentative agents and set Cooperate of cooperative agents; every Ag must reach a consensus on its arguments with agents in Argue, and Ag may ask for arguments from agents in Cooperate to complete its partial arguments. The argumentation-based negotiation proposal allows the modelling a hierarchy of knowledge bases representing, for instance, a business's organization or a taxonomy of some subject, and also an MAS where each agent represents "acquired knowledge" in a different period of time. Furthermore, any agent in an MAS can be queried regarding the truth value of some belief. It depends on from which agent such a belief is inferred, and also what the specification in both Argue and Cooperate is, given the overall agents in the MAS. However, such an answer will always be consistent/paraconsistent with the agents' knowledge base involved. This dissertation proposes a (declarative and operational) argumentation semantics for an agent's knowledge base. Furthermore, it proposes a declarative argumentation-based negotiation semantics for a multi-agent setting, which uses most of the definitions from the former semantics