Simplification of many-valued logic formulas using anti-links

We present the theoretical foundations of the many-valued generalization of a technique for simplifying large non-clausal formulas in propositional logic, that is called "removal of anti-links". Possible applications of anti-links include computation of prime implicates of large non-clausal formulas as required, for example, in diagnosis. Anti-links do not compute any normal form of a given formula themselves, rather, they remove certain forms of redundancy from formulas in negation normal form (NNF). Their main advantage is that no clausal normal form has to be computed in order to remove redundant parts of a formula. In this paper, we define an anti-link operation on a generic language for expressing many-valued logic formulas called "signed NNF" and we show that all interesting properties of two-valued anti-links generalize to the many-valued setting, although in a non-trivial way

Many-Valued Hybrid Logic

In this paper we define a family of many-valued semantics for hybrid logic, where each semantics is based on a finite Heyting algebra of truth-values. We provide sound and complete tableau systems for these semantics. Moreover, we show how the tableau systems can be made terminating and thereby give rise to decision procedures for the logics in question. Our many-valued hybrid logics turn out to be "intermediate" logics between intuitionistic hybrid logic and classical hybrid logic in a specific sense explained in the paper. Our results show that many-valued hybrid logic is indeed a natural enterprise

On the generation of equational dynamic logics for weighted imperative programs

Dynamic logic is a powerful framework for reasoning about imperative programs. This paper extends previous work [9] on the systematic generation of dynamic logics from the propositional to the equational case, to capture `full- edged' imperative programs. The generation process is parametric on a structure specifying a notion of `weight' assigned to programs. The paper introduces also a notion of bisimilarity on models of the generated logics, which is shown to entail modal equivalence with respect to the latter.POCI-01-0145-FEDER-030947. ERDF—European Regional Development Fund through the Operational Programme for Competitiveness and Internationalisation - COMPETE 2020 Programme and by National Funds through the Portuguese funding agency, FCT - Fundação para a Ciência e a Tecnologia, within project POCI-01-0145-FEDER-030947. The second author is supported in the scope of the framework contract foreseen in the numbers 4, 5 and 6 of the article 23, of the Decree-Law 57/2016, of August 29, changed by Portuguese Law 57/2017, of July 19 and by UID/MAT/04106/2019 at CIDM

Non-clausal multi-ary alpha-generalized resolution calculus for a finite lattice-valued logic

Due to the need of the logical foundation for uncertain information processing, development of efficient automated reasoning system based on non-classical logics is always an active research area. The present paper focuses on the resolution-based automated reasoning theory in a many-valued logic with truth-values defined in a lattice-ordered many-valued algebraic structure - lattice implication algebras (LIA). Specifically, as a continuation and extension of the established work on binary resolution at a certain truth-value level α (called α-resolution), a non-clausal multi-ary α-generalized resolution calculus is introduced for a lattice-valued propositional logic LP(X) based on LIA, which is essentially a non-clausal generalized resolution avoiding reduction to normal clausal form. The new resolution calculus in LP(X) is then proved to be sound and complete. The concepts and theoretical results are further extended and established in the corresponding lattice-valued first-order logic LF(X) based on LIA

Fusing uncertain knowledge and evidence for maritime situational awareness via Markov Logic Networks

The concepts of event and anomaly are important building blocks for developing a situational picture of the observed environment. We here relate these concepts to the JDL fusion model and demonstrate the power of Markov Logic Networks (MLNs) for encoding uncertain knowledge and compute inferences according to observed evidence. MLNs combine the expressive power of first-order logic and the probabilistic uncertainty management of Markov networks. Within this framework, different types of knowledge (e.g. a priori, contextual) with associated uncertainty can be fused together for situation assessment by expressing unobservable complex events as a logical combination of simpler evidences. We also develop a mechanism to evaluate the level of completion of complex events and show how, along with event probability, it could provide additional useful information to the operator. Examples are demonstrated on two maritime scenarios of rules for event and anomaly detection

Grafting Hypersequents onto Nested Sequents

We introduce a new Gentzen-style framework of grafted hypersequents that combines the formalism of nested sequents with that of hypersequents. To illustrate the potential of the framework, we present novel calculi for the modal logics $\mathsf{K5}$ and $\mathsf{KD5}$, as well as for extensions of the modal logics $\mathsf{K}$ and $\mathsf{KD}$ with the axiom for shift reflexivity. The latter of these extensions is also known as $\mathsf{SDL}^+$ in the context of deontic logic. All our calculi enjoy syntactic cut elimination and can be used in backwards proof search procedures of optimal complexity. The tableaufication of the calculi for $\mathsf{K5}$ and $\mathsf{KD5}$ yields simplified prefixed tableau calculi for these logic reminiscent of the simplified tableau system for $\mathsf{S5}$, which might be of independent interest

A Constrained, Possibilistic Logical Approach for Software System Survivability Evaluation

In this paper, we present a logical framework to facilitate users in assessing a software system in terms of the required survivability features. Survivability evaluation is essential in linking foreign software components to an existing system or obtaining software systems from external sources. It is important to make sure that any foreign components/systems will not compromise the current system’s survivability properties. Given the increasing large scope and complexity of modern software systems, there is a need for an evaluation framework to accommodate uncertain, vague, or even ill-known knowledge for a robust evaluation based on multi-dimensional criteria. Our framework incorporates user-defined constrains on survivability requirements. Necessity-based possibilistic uncertainty and user survivability requirement constraints are effectively linked to logic reasoning. A proof-of-concept system has been developed to validate the proposed approach. To our best knowledge, our work is the first attempt to incorporate vague, imprecise information into software system survivability evaluation