Yoni Zohar

SAT-Based Decision Procedure for Analytic Pure Sequent Calculi

We identify a wide family of analytic sequent calculi for propositional non-classical logics whose derivability problem can be uniformly reduced to SAT. The proposed reduction is based on interpreting these calculi using non-deterministic semantics. Its time complexity is polynomial, and, in fact, linear for a useful subfamily. We further study an extension of such calculi with Next operators, and show that this extension preserves analyticity and is subject to a similar reduction to SAT. A particular interesting instance of these results is a HORNSAT-based linear-time decision procedure for Gurevich and Neeman’s primal infon logic and several natural extensions of it.

Sequent Systems for Negative Modalities

Non-classical negations may fail to be contradictory-forming operators in more than one way, and they often fail also to respect fundamental meta-logical properties such as the replacement property. Such drawbacks are witnessed by intricate semantics and proof systems, whose philosophical interpretations and computational properties are found wanting. In this paper we investigate congruential non-classical negations that live inside very natural systems of normal modal logics over complete distributive lattices; these logics are further enriched by adjustment connectives that may be used for handling reasoning under uncertainty caused by inconsistency or undeterminedness. Using such straightforward semantics, we study the classes of frames characterized by seriality, reflexivity, functionality, symmetry, transitivity, and some combinations thereof, and discuss what they reveal about sub-classical properties of negation. To the logics thereby characterized we apply a general mechanism that allows one to endow them with analytic ordinary sequent systems, most of which are even cut-free. We also investigate the exact circumstances that allow for classical negation to be explicitly defined inside our logics.

Online detection of effectively callback free objects with applications to smart contracts

Callbacks are essential in many programming environments, but drastically complicate program understanding and reasoning because they allow to mutate objects local states by external objects in unexpected fashions, thus breaking modularity. The famous DAO bug in the cryptocurrency framework Ethereum, employed callbacks to steal

Non-Deterministic Matrices in Action: Expansions, Refinements, and Rexpansions

150M. We define the notion of Effectively Callback Free (ECF) objects in order to allow callbacks without preventing modular reasoning. An object is ECF in a given execution trace if there exists an equivalent execution trace without callbacks to this object. An object is ECF if it is ECF in every possible execution trace. We study the decidability of dynamically checking ECF in a given execution trace and statically checking if an object is ECF. We also show that dynamically checking ECF in Ethereum is feasible and can be done online. By running the history of all execution traces in Ethereum, we were able to verify that virtually all existing contract executions, excluding these of the DAO or of contracts with similar known vulnerabilities, are ECF. Finally, we show that ECF, whether it is verified dynamically or statically, enables modular reasoning about objects with encapsulated state.

‘Mathematical’ Does Not Mean ‘Boring’: Integrating Software Assignments to Enhance Learning of Logico-Mathematical Concepts

The operations ofexpansion and refinement on non-deterministic matrices(Nmatrices) are composed to form a new operation called rexpansion. Properties of this operation are investigated, together with their effects on the induced consequence relations. A semantic method for obtaining conservative extensions of matrix-defined logics is introduced and applied to fragments of the classical two-valued matrix, as well as to other well-known many-valued matrices. The central application of rexpansion that we present is the construction of truth-preserving paraconsistent conservative extensions of Gödel fuzzy logic.

On the Construction of Analytic Sequent Calculi for Sub-classical Logics

Insufficient mathematical skills of practitioners are hypothesized as one of the main hindering factors for the adoption of formal methods in industry. This problem is directly related to negative attitudes of future computing professionals to core mathematical disciplines, which are perceived as difficult, boring and not relevant to their future daily practices. This paper is a contribution to the ongoing debate on how to make courses in Logic and Formal Methods both relevant and engaging for future software practitioners. We propose to increase engagement and enhance learning by integrating ‘hands-on’ software engineering assignments based on cross-fertilization between software engineering and logic. As an example, we report on a pilot assignment given at a Logic and Formal Methods course for Information Systems students at the University of Haifa. We describe the design of the assignment, students’ feedback and discuss some lessons learnt from the pilot.

From the subformula property to cut-admissibility in propositional sequent calculi

We study the question of when a given set of derivable rules in some basic analytic propositional sequent calculus forms itself an analytic calculus. First, a general syntactic criterion for analyticity in the family of pure sequent calculi is presented. Next, given a basic calculus admitting this criterion, we provide a method to construct weaker pure calculi by collecting simple derivable rules of the basic calculus. The obtained calculi are analytic-by-construction. While the criterion and the method are completely syntactic, our proofs are semantic, based on interpretation of sequent calculi via non-deterministic valuation functions. In particular, this method captures calculi for a wide variety of paraconsistent logics, as well as some extensions of Gurevich and Neemans primal infon logic.

Cut-Admissibility as a Corollary of the Subformula Property

While the subformula property is usually a trivial consequence of cut-admissibility in sequent calculi, it is unclear in which cases the subformula property implies cut-admissibility. In this paper, we identify two wide families of propositional sequent calculi for which this is the case: the (generalized) subformula property is equivalent to cutadmissibility. For this purpose, we employ a semantic criterion for cut-admissibility, which allows us to uniformly handle a wide variety of calculi. Our results shed light on the relation between these two fundamental properties of sequent calculi, and can be useful to simplify cut-admissibility proofs in various calculi for non-classical logics, where the subformula property (equivalently, the property known as “analytic cut-admissibility”) is easier to show than cut-admissibility.1 Keywords— Sequent Calculus, Subformula Property, Cut-elimination, Analyticity

Correction to: Sequent Systems for Negative Modalities

We identify two wide families of propositional sequent calculi for which cut-admissibility is a corollary of the subformula property. While the subformula property is often a simple consequence of cut-admissibility, our results shed light on the converse direction, and may be used to simplify cut-admissibility proofs in various propositional sequent calculi. In particular, the results of this paper may be used in conjunction with existing methods that establish the subformula property, to obtain that cut-admissibility holds as well.

Gen2sat: An Automated Tool for Deciding Derivability in Analytic Pure Sequent Calculi

In the original publication, the corresponding author was indicated incorrectly. The correct corresponding author of the article should be Ori Lahav. The original article has been updated accordingly.