11 research outputs found
Complexity Jumps In Multiagent Justification Logic Under Interacting Justifications
The Logic of Proofs, LP, and its successor, Justification Logic, is a
refinement of the modal logic approach to epistemology in which
proofs/justifications are taken into account. In 2000 Kuznets showed that
satisfiability for LP is in the second level of the polynomial hierarchy, a
result which has been successfully repeated for all other one-agent
justification logics whose complexity is known.
We introduce a family of multi-agent justification logics with interactions
between the agents' justifications, by extending and generalizing the two-agent
versions of the Logic of Proofs introduced by Yavorskaya in 2008. Known
concepts and tools from the single-agent justification setting are adjusted for
this multiple agent case. We present tableau rules and some preliminary
complexity results. In several cases the satisfiability problem for these
logics remains in the second level of the polynomial hierarchy, while for
others it is PSPACE or EXP-hard. Furthermore, this problem becomes PSPACE-hard
even for certain two-agent logics, while there are EXP-hard logics of three
agents
Decidability for some justification logics with negative introspection
Justification logics are modal logics that include justifications for the agent's knowledge. So far, there are no decidability results available for justification logics with negative introspection. In this paper, we develop a novel model construction for such logics and show that justification logics with negative introspection are decidable for finite constant specification
TR-2014003: On the Complexity of Two-Agent Justification Logic
We investigate the complexity of derivability for two-agent Justification Logic. For this purpose we revisit Yavorskaya’s two-agent LP with interactions (2008), we simplify the syntax and provide natural extensions. We consider two-agent versions of other justification logics as well as ways to combine two justification logics. For most of these cases we prove that the upper complexity bound established for the single-agent cases are maintained: these logics ’ derivability problem is in the second step of the polynomial hierarchy. For certain logics, though, we discover a complex-ity jump to PSPACE-completeness, which is a new phenomenon for Justification Logic
Teoria tradicional da informação semântica sem escândalo da dedução : uma reavaliação moderadamente externalista do tópico baseada em semântica urna e uma aplicação paraconsistente
Orientador: Walter Alexandre CarnielliTese (doutorado) - Universidade Estadual de Campinas, Instituto de Filosofia e Ciências HumanasResumo: A presente tese mostra que é possÃvel reestabelecer a teoria tradicional da informação semântica (no que segue apenas TSI, originalmente proposta por Bar-Hillel e Carnap (1952, 1953)) a partir de uma descrição adequada das condições epistemológicas de nossa competência semântica. Uma consequência clássica de TSI é o assim chamado escândalo da dedução (no que segue SoD), tese segundo a qual verdades lógicas têm quantidade nula de informação. SoD é problemático dado que conflita com o caráter ampliativo do conhecimento formal. Baseado nisso, trabalhos recentes (e.g., Floridi (2004)) rejeitam TSI apesar de suas boas intuições sobre a natureza da informação semântica. Por outro lado, esta tese reconsidera a estratégia de assumir a semântica urna (RANTALA, 1979) como o pano de fundo metateórico privilegiado para o reestabelecimento de TSI sem SoD. A presente tese tem o seguinte plano. O capÃtulo 1 introduz o plano geral da tese. No capÃtulo 2, valendo-se fortemente de trabalhos clássicos sobre o externalismo semântico, eu apresento algum suporte filosófico para essa estratégia ao mostrar que a semântica urna corretamente caracteriza as condições epistemológicas de nossa competência semântica no uso de quantificadores. O capitulo 3 oferece uma descrição precisa da semântica urna a partir da apresentação de suas definições básicas e alguns de seus teoremas mais funda- mentais. No capÃtulo 4, eu me concentro mais uma vez no tema da informação semântica ao formalizar TSI em semântica urna e provar que nesse contexto SoD não vale. Finalmente, nos capÃtulos 5 e 6 eu considero resultados modelo-teóricos mais avançados sobre semântica urna e exploro uma possÃvel aplicação paraconsistente das ideias principais dessa tese, respectivamenteAbstract: This thesis shows that it is possible to reestablish the traditional theory of semantic information (TSI, originally proposed by Bar-Hillel and Carnap (1952, 1953)) by providing an adequate account of the epistemological conditions of our semantic competence. A classical consequence of TSI is the so-called scandal of deduction (hereafter SoD) according to which logical truths have null amount of information. SoD is problematic since it does not make room for the ampliative character of formal knowledge. Based on this, recent work on the subject (e.g., Floridi (2004)) rejects TSI despite its good insights on the nature of semantic information. On the other hand, this work reconsiders the strategy of taking urn semantics (RANTALA, 1979) as a privileged metatheoretic framework for the formalization of TSI without SoD. The present thesis is planned in the following way. Chapter 1 introduces the thesis¿ overall plan. In chapter 2, relying heavily on classical works on semantic externalism, I present some philosophical support for this strategy by showing that urn semantics correctly characterizes the epistemological conditions of our semantic competence in the use of quantifiers. Chapter 3 offers a precise description of urn semantics by characterizing its basic definitions and some of its most fundamental theorems. In chapter 4, turning the focus once again to semantic information, I formalize TSI in urn semantics and show that in this context SoD does not hold. Finally, in chapter 5 and 6 I consider more advanced model-theoretic results on urn semantics and explore a paraconsistent possible application of the present idea, respectivelyDoutoradoFilosofiaDoutor em Filosofia142038/2014-8CNP
Logical Omniscience as a Computational Complexity Problem
The logical omniscience feature assumes that an epistemic agent knows all logical consequences of her assumptions. This paper offers a general theoretical framework that views logical omniscience as a computational complexity problem. We suggest the following approach: we assume that the knowledge of an agent is represented by an epistemic logical system E; we call such an agent not logically omniscient if for any valid knowledge assertion A of type F is known, a proof of F in E can be found in polynomial time in the size of A. We show that agents represented by major modal logics of knowledge and belief are logically omniscient, whereas agents represented by justification logic systems are not logically omniscient with respect to t is a justification for F