Temporal Justification Logic

Justification logics are modal-like logics with the additional capability of recording the reason, or justification, for modalities in syntactic structures, called justification terms. Justification logics can be seen as explicit counterparts to modal logics. The behavior and interaction of agents in distributed system is often modeled using logics of knowledge and time. In this paper, we sketch some preliminary ideas on how the modal knowledge part of such logics of knowledge and time could be replaced with an appropriate justification logic

Intransitive temporal multi-agent’s logic, knowledge and uncertainty, plausibility

© Springer International Publishing Switzerland 2016. We study intransitive temporal logic implementing multiagent’s approach and formalizing knowledge and uncertainty. An innovative point here is usage of non-transitive linear time and multi-valued models - the ones using separate valuations Vj for agent’s knowledge of facts and summarized (agreed) valuation together with rules for computation truth values for compound formulas. The basic mathematical problems we study here are - decidability and decidability w.r.t. admissible rules. First, we study general case - the logic with non-uniform intransitivity and solve its decidability problem. Also we consider a modification of this logic - temporal logic with uniform non-transitivity and solve problem of recognizing admissibility in this logic

Semirings of Evidence

In traditional justification logic, evidence terms have the syntactic form of polynomials, but they are not equipped with the corresponding algebraic structure. We present a novel semantic approach to justification logic that models evidence by a semiring. Hence justification terms can be interpreted as polynomial functions on that semiring. This provides an adequate semantics for evidence terms and clarifies the role of variables in justification logic. Moreover, the algebraic structure makes it possible to compute with evidence. Depending on the chosen semiring this can be used to model trust, probabilities, cost, etc. Last but not least the semiring approach seems promising for obtaining a realization procedure for modal fixed point logics

Should We Embrace Impossible Worlds Due to the Flaws of Normal Modal Logic?

Some philosophers advance the claim that the phenomena of logical omniscience and of the indiscernibility of metaphysical statements, which arise in (certain) interpretations of normal modal logic, provide strong reasons in favour of impossible world approaches. These two specific lines of argument will be presented and discussed in this paper. Contrary to the recent much-held view that the characteristics of these two phenomena provide us with strong reasons to adopt impossible world approaches, the view defended here is that no such ‘knock-down arguments’ do emanate on those grounds. This is not to rule out that there cannot be any other good reasons for assuming impossible world semantics. However, the discussion of a further argument for impossible worlds will suggest that different attempts to argue for them likely present intertwined problems

Justification Logic, Semirings and Realizations

The evidence terms in traditional justification logic have the form of polynomials, but semantically this structure is ignored by assigning a set of formulas to each term. We introduced the logic SE and the corresponding semantics, where terms are mapped to actual polynomials over a semiring. This gives a clear distinction between constants and variables, because constants in a term are mapped to elements in the semiring, yielding a function in the variables of the term. Further it is possible to compute with justifications. This can be used to model trust (Viterbi semiring), probabilities (powerset semiring), cost (tropical semiring), etc., depending on the chosen semiring. For the logic SE and its semantics we prove soundness and completeness. The completeness proof does not follow the standard line with maximal consistent sets. Instead we used a mapping to classical propositional logic, which basically replaces formulas of the form t : A by a fresh atomic proposition. Then we clarified the relationship between SE and the modal logic K by two realization theorems. The proof of the first one is closely related to a realization procedure without +, found by Kuznets. Then we considered ω-continuous semirings with the motivation that every Scott-continuous function on such a semiring has a fixed point, which can be used to establish a connection between common knowledge and justification logic. We therefore introduced the logic SEK with its semantics and proved soundness and completeness in a similar way as before. The main difference between SE and SEK is that the latter uses the polynomials over a semiring directly as justification terms. Apart from simplifying a lot this change was necessary for using the fixed points, because a fixed point is given by the (infinite) ascending Kleene chain, which would result in an infinite term. The infinite sum operation on the justification terms turned out to be too complex for common knowledge itself. For example terms for E0, E2, E4 and so on can be added to create a term for ΣnϵN E2n, which has no finite representation in common knowledge. We therefore introduced the system SAx (as an extension of common knowledge), which allows arbitrary sets of words of modal operators. Working towards a realization theorem we found a way of addressing occurrences of subformulas by a 0-1-sequence. This made the proof significantly more rigorous. When we dealt with the modus ponens rule we saw that all the applications of MP in a proof created a system of equations of the form x = f(x). We therefore used the fixed point theorem and got a realization algorithm that realizes the modus ponens rule directly and yields a normal realization. In the future it could be interesting to try to generalize this approach. By using fixed points one could find a realization procedure for more general modal fixed point logics including the modal μ-calculus

Contribution to the evaluation and optimization of passengers' screening at airports

Security threats have emerged in the past decades as a more and more critical issue for Air Transportation which has been one of the main ressource for globalization of economy. Reinforced control measures based on pluridisciplinary research and new technologies have been implemented at airports as a reaction to different terrorist attacks. From the scientific perspective, the efficient screening of passengers at airports remain a challenge and the main objective of this thesis is to open new lines of research in this field by developing advanced approaches using the resources of Computer Science. First this thesis introduces the main concepts and definitions of airport security and gives an overview of the passenger terminal control systems and more specifically the screening inspection positions are identified and described. A logical model of the departure control system for passengers at an airport is proposed. This model is transcribed into a graphical view (Controlled Satisfiability Graph-CSG) which allows to test the screening system with different attack scenarios. Then a probabilistic approach for the evaluation of the control system of passenger flows at departure is developped leading to the introduction of Bayesian Colored Petri nets (BCPN). Finally an optimization approach is adopted to organize the flow of passengers at departure as best as possible given the probabilistic performance of the elements composing the control system. After the establishment of a global evaluation model based on an undifferentiated serial processing of passengers, is analyzed a two-stage control structure which highlights the interest of pre-filtering and organizing the passengers into separate groups. The conclusion of this study points out for the continuation of this theme

Interactions and Complexity in Multi-Agent Justification Logic

Justification cation Logic is the logic which introduces justifications to the epistemic setting. In contrast to Modal Logic, when an agent believes (or knows) a certain claim, in Justification Logic we assume the agent believes the claim because of a certain justification. Therefore, instead of having formulas that represent the belief of a claim (ex. □ø or Kø), we have formulas that represent that the belief of a claim follows from a provided justification (ex. t : ø). The original Justification Logic is LP, the Logic of Proofs, and was introduced by Artemov in 1995 as a link between Intuitionistic Truth and Gödel proofs in Peano Arithmetic. The complexity of Justification Logic was first studied by Kuznets in 2000. He demonstrated that for many justification logics, their derivability problem (and thus their satisfiability problem) is in the second level of the Polynomial Hierarchy, a result which was shown to be tight and which was later extended to more justification logics. In fact, so far, given reasonable assumptions, every single-agent justification logic whose complexity has been settled has its satisfiability problem in the second level of the Polynomial Hierarchy. This result is nicely contrasted to Modal Logic, as the corresponding modal systems are PSPACE-complete. We investigate the complexity of Justification Logic and Modal Logic when we allow multiple agents whose justifications affect each other -- by including some combination of the axioms t :iø → t :jø and t :iø → !t :j t :iø (modal cases: □iø→ □jø). We discover complexity jumps new for the field of Justification Logic: in addition to logics with their satisfiability problem in the second level of the polynomial hierarchy (as is the usual case until now), there are logics that have PSPACE-complete, EXP-complete and even NEXP-complete satisfiability problems. It is notable how the behavior of several of these justification logics mirrors the behavior of the corresponding multi-modal logics when we restrict modal formulas (in negation normal form) to use no diamonds. Thus we first study the complexity of such diamond-free modal logics and then we deduce complexity properties for the justification logic systems. On the other hand, it is similarly notable how certain lower complexity bounds -- the NEXP-hardness bound and the general Σp2-hardness bound we present -- are more dependent on the behavior of the justifications. The complexity results are interesting for Modal Logic as well, as we give hardness results that hold even for the diamond-free, 1-variable fragments of these multi-modal logics and then we determine the complexity of these logics in a general case

Autoridade, incerteza e responsabilidade : ensaios sobre a legitimidade do regulador à luz da Grande Crise

A presente tese é composta de seis artigos independentes entre si, agrupados como capítulos em duas seções, de acordo com a similaridade do tema. A primeira parte trata de problemas filosóficos relacionados à teoria da autoridade jurídica de Raz e à teoria da decisão racional. A segunda parte trata, principalmente, da atuação de autoridades regulatórias em situações de incerteza – em especial, usando como exemplo a atuação de Bancos Centrais no contexto da Crise de 2008. Abordam-se, respectivamente: o paradoxo do desacordo (a potencial inconsistência em discordar de uma autoridade legítima), a refutação de Raz à incorporação de conceitos morais ao direito, o problema da incerteza e futuros contingentes, a legitimidade da autoridade em situações de incerteza, a objeção fatalista à reprovação moral por eventos econômicos, e a necessidade de instituir sanções para dissuadir financistas a assumirem riscos excessivos.This dissertation is made of six independent articles, grouped as chapters in two parts, according to similarities between their themes. The first part deals with philosophical problems related to Raz's theory of legal authority and to rational decision theory. The second part deals mainly with the performance of regulatory authorities in situations of uncertainty - in particular, using as example the performance of Central Banks in the context of the 2008 Crisis. We discuss, in order: the paradox of disagreement (the potential inconsistency of disagreeing with a legitimate authority), Raz's refutation to the incorporation of moral concepts into law, the problem of uncertainty and future contingents, the legitimacy of authority in situations of uncertainty, the fatalistic objection to moral disapproval for economic events, and the need to impose sanctions to deter finance investors from taking excessive risks