Not All Bugs Are Created Equal, But Robust Reachability Can Tell the Difference

This paper introduces a new property called robust reachability which refines the standard notion of reachability in order to take replicability into account. A bug is robustly reachable if a controlled input can make it so the bug is reached whatever the value of uncontrolled input. Robust reachability is better suited than standard reachability in many realistic situations related to security (e.g., criticality assessment or bug prioritization) or software engineering (e.g., replicable test suites and flakiness). We propose a formal treatment of the concept, and we revisit existing symbolic bug finding methods through this new lens. Remarkably, robust reachability allows differentiating bounded model checking from symbolic execution while they have the same deductive power in the standard case. Finally, we propose the first symbolic verifier dedicated to robust reachability: we use it for criticality assessment of 4 existing vulnerabilities, and compare it with standard symbolic execution.

Admissible Inference Rules and Semantic Property of Modal Logics

Firstly semantic property of nonstandart logics were described by formulas which are peculiar to studied a models in general, and do not take to consideration a variable conditions and a changing assumptions. Evidently the notion of inference rule generalizes the notion of formulas and brings us more flexibility and more expressive power to model human reasoning and computing. In 2000-2010 a few results on describing of explicit bases for admissible inference rules for nonstandard logics (S4, K4, H etc.) appeared. The key property of these logics was weak co-cover property. Beside the improvement of deductive power in logic, an admissible rule are able to describe some semantic property of given logic. We describe a semantic property of modal logics in term of admissibility of given set of inference rules. We prove that modal logic over logic 𝐺𝐿 enjoys weak co-cover property iff all given rules are admissible for logic.

Improved characterisation of MRSA transmission using within-host bacterial sequence diversity

Methicillin-resistant Staphylococcus aureus (MRSA) transmission in the hospital setting has been a frequent subject of investigation using bacterial genomes, but previous approaches have not yet fully utilised the extra deductive power provided when multiple pathogen samples are acquired from each host. Here, we used a large dataset of MRSA sequences from multiply-sampled patients to reconstruct colonisation of individuals in a high-transmission setting in a hospital in Thailand. We reconstructed transmission trees for MRSA. We also investigated transmission between anatomical sites on the same individual, finding that this either occurs repeatedly or involves a wide transmission bottleneck. We examined the between-subject bottleneck, finding considerable variation in the amount of diversity transmitted. Finally, we compared our approach to the simpler method of identifying transmission pairs using single nucleotide polymorphism (SNP) counts. This suggested that the optimum threshold for identifying a pair is 39 SNPs, if sensitivities and specificities are equally weighted.

Modeling of Social Welfare Functions in J. Rawls’s Theory of Justice

Public policy is directly related to the formulation of social goals. Social welfare functions can be modeled in two ways: (a) as a derivative of the social status ordering mechanisms applied in public policy; or (b) as norms, which must be further strengthened by solid theoretical foundation. Normative SWF modeling variants, which include Rawls’s theory of justice, are characterized by simplicity and deductive power. This article examines how Rawls’s critique of utilitarianism and intuitionism doctrines allowed changing the axis of political decision-making, reinforcing the priority of the idea of justice. It is also argued that the internal structural logic of this new priority better suits social minorities and that under its banner they are more active and successful in representing their interests in the political arena than the majorities of the same societies.

Towards applied theories based on computability logic

Computability logic (CL) is a recently launched program for redeveloping logic as a formal theory of computability, as opposed to the formal theory of truth that logic has more traditionally been. Formulas in it represent computational problems, “truth” means existence of an algorithmic solution, and proofs encode such solutions. Within the line of research devoted to finding axiomatizations for ever more expressive fragments of CL, the present paper introduces a new deductive system CL12 and proves its soundness and completeness with respect to the semantics of CL. Conservatively extending classical predicate calculus and offering considerable additional expressive and deductive power, CL12 presents a reasonable, computationally meaningful, constructive alternative to classical logic as a basis for applied theories. To obtain a model example of such theories, this paper rebuilds the traditional, classical-logicbased Peano arithmetic into a computability-logic-based counterpart. Among the purposes of the present contribution is to provide a starting point for what, as the author wishes to hope, might become a new line of research with a potential of interesting findings—an exploration of the presumably quite unusual metatheory of CL-based arithmetic and other CL-based applied systems.

Inductive Logic Programming in Databases: From Datalog to

In this paper we address an issue that has been brought to the attention of the database community with the advent of the Semantic Web, i.e., the issue of how ontologies (and semantics conveyed by them) can help solving typical database problems, through a better understanding of Knowledge Representation (KR) aspects related to databases. In particular, we investigate this issue from the ILP perspective by considering two database problems, (i) the definition of views and (ii) the definition of constraints, for a database whose schema is represented also by means of an ontology. Both can be reformulated as ILP problems and can benefit from the expressive and deductive power of the KR framework $\mathcal{DL}+log}^{\neg\vee}$. We illustrate the application scenarios by means of examples.

Building Rules on Top of Ontologies for the Semantic Web with Inductive Logic Programming

Building rules on top of ontologies is the ultimate goal of the logical layer of the Semantic Web. To this aim, an ad-hoc markup language for this layer is currently under discussion. It is intended to follow the tradition of hybrid knowledge representation and reasoning systems, such as$\mathcal{AL}$-log that integrates the description logic$\mathcal{ALC}$and the function-free Horn clausal languageDatalog. In this paper, we consider the problem of automating the acquisition of these rules for the Semantic Web. We propose a general framework for rule induction that adopts the methodological apparatus of Inductive Logic Programming and relies on the expressive and deductive power of$\mathcal{AL}$-log. The framework is valid whatever the scope of induction (description versus prediction) is. Yet, for illustrative purposes, we also discuss an instantiation of the framework which aims at description and turns out to be useful in Ontology Refinement.

A New Rule of Inference for an Epistemic Logic Applied to Cognitive Psychology

Though psychology's only hope of ever becoming a science resides in a phenomenological approach, no mathematical logic presently exists for formalizing adequately a comprehensive cognitive psychology. Such a needed epistemic logic would lose some rules of inference which positivistic, nonepistemic mathematical logics employ. Therefore, if this needed new logic is to provide sufficient deductive power, new rules of inference would be required. The present paper attempts to develop one such new rule of inference.