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We provide a complete axiomatization of modal inclusion logic - team-based modal logic extended with inclusion atoms. We review and refine an expressive completeness and normal form theorem for the logic, define a natural deduction proof…

Sound and complete axiomatizations are provided for a number of different logics involving modalities for knowledge and time. These logics arise from different choices for various parameters. All the logics considered involve the discrete…

In this paper we examine the problem of computing majority function $\mathrm{MAJ}_n$ on $n$ bits by depth-two formula, where each gate is a majority function on at most $k$ inputs. We present such formula that gives the first nontrivial…

Axiomatizing mathematical structures is a goal of Mathematical Logic. Axiomatizability of the theories of some structures have turned out to be quite difficult and challenging, and some remain open. However axiomatization of some…

Majority vote is a basic method for amplifying correct outcomes that is widely used in computer science and beyond. While it can amplify the correctness of a quantum device with classical output, the analogous procedure for quantum output…

Axiomatic approach has demonstrated its power in mathematics. The main goal of this preprint is to show that axiomatic methods are also very efficient for computer science. It is possible to apply these methods to many problems in computer…

Axiomatizing mathematical structures and theories is an objective of Mathematical Logic. Some axiomatic systems are nowadays mere definitions, such as the axioms of Group Theory; but some systems are much deeper, such as the axioms of…

May's Theorem [K. O. May, Econometrica 20 (1952) 680-684] characterizes majority voting on two alternatives as the unique preferential voting method satisfying several simple axioms. Here we show that by adding some desirable axioms to…

Like many other voting systems, Majority Judgement suffers from the weaknesses of the underlying mathematical model: Elections as problem of choice or ranking. We show how the model can be enhanced to take into account the complete process…

The initial majority identification task is a fundamental test problem in cellular automaton research. To pass the test, an automaton must evolve to a uniform configuration consisting of the state that was in the majority for any initial…

We know extensions of first order logic by quantifiers of the kind "there are uncountable many ...", "most ..." with new axioms and appropriate semantics. Related are operations such as "set of x, such that ...", Hilbert's…

Accretive and monotone operator theory are central branches of nonlinear functional analysis and constitute the abstract study of set-valued mappings between function spaces. This paper deals with the computational properties of certain…

Inclusion logic is a variant of dependence logic that was shown to have the same expressive power as positive greatest fixed-point logic. Inclusion logic is not axiomatizable in full, but its first-order consequences can be axiomatized. In…

In this paper we present {\em refinement modal logic}. A refinement is like a bisimulation, except that from the three relational requirements only `atoms' and `back' need to be satisfied. Our logic contains a new operator 'all' in addition…

Balancing model complexity against the information contained in observed data is the central challenge to learning. In order for complexity-efficient models to exist and be discoverable in high dimensions, we require a computational…

In nanoelectronic circuit synthesis, the majority gate and the inverter form the basic combinational logic primitives. This paper deduces the mathematical formulae to estimate the logical masking capability of majority gates, which are used…

Recent authors have proposed analyzing conditional reasoning through a notion of intervention on a simulation program, and have found a sound and complete axiomatization of the logic of conditionals in this setting. Here we extend this…

Justification logics are special kinds of modal logics which provide a framework for reasoning about epistemic justifications. For this, they extend classical boolean propositional logic by a family of necessity-style modal operators "t:",…

In the present paper syntax and semantics will be presented for an expansion of ordinary n-agent QML with constant domain, non-rigid constants, rigid variables and including both functions, relations, and equality. Further, the number of…

Equilibrium logic is an approach to nonmonotonic reasoning that extends the stable-model and answer-set semantics for logic programs. In particular, it includes the general case of nested logic programs, where arbitrary Boolean combinations…