The paper considers the task of bot detection in social networks. It checks the hypothesis that bots break Benford’s law much more often than users, so one can identify them. A bot detection approach is proposed based on experiments where the test results for bot datasets of different classes and real-user datasets of different communities are evaluated and compared. The experiments show that automatically controlled bots possibly can be identified by disagreement with Benford’s law, while human-orchestrated bots are not.

The automorphism groups of types in several systems of type theory are studied. It is shown that in simply typed λ-calculus λ1βη and in its extension with surjective pairing and terminal object these groups correspond exactly to the groups of automorphisms of finite trees. In second-order λ-calculus and in Luo's framework (LF) with dependent products, any finite group may be represented.

This paper deals with model transformations based on attributed graphs transformation. Our approach is based on the categorical approach called Single Pushout. The principal goal being to strengthen the attribute computation part, we generalize our earlier approach based on the use of typed lambda-terms with inductive types and recursion to represent attributes and computation functions. The generalized approach takes terms in variable context as attributes and partial proofs as computation functions that permit to combine computation with proof development and verification. The intended domains of application are the development of cerified software models and semantics models for interactive proof development and verification.

The problem of the commutativity of algebraic (categorical) diagrams has attracted the attention of researchers for a long time. For example, the related notion of coherence was discussed in Mac Lane's homology book Mac Lane (1963), see also his AMS presidential address Mac Lane (1976). Researchers in category theory view this problem from a specific angle, and for them it is not just a question of convenient notation, though it is worth mentioning the important role that notation plays in the development of science (take, for example, the progress made after the introduction of symbolic notation in logics or matrix notation in algebra). In 1976, Peter Freyd published the paper ‘Properties Invariant within Equivalence Types of Categories’ (Freyd 1976), where the central role is played by the notion of a ‘diagrammatic property’. We may also recall the process of ‘diagram chasing’, and its applications in topology and algebra. But before we can use diagrams (and the principal property of a diagram is its commutativity), it is vital for us to be able to check whether a diagram is commutative.

Isomorphisms of types are computational witnesses of logical equivalence with additional properties. The types/formulas A and B are isomorphic if there are functions (in a certain formalism) f : A → B and g : B → A such that g ○ f and f ○ g are equal in a certain sense to the identity on A and B, respectively. Typical such formalisms are extensions of simply typed λ-calculus, with βη-convertibility as equality relation. Another view of a pair of functions f : A → B and g : B → A (besides establishing the logical equivalence of A and B) is that f is invertible with left-inverse g, and it is then natural to relax the above symmetric condition to just g ○ f being equal to the identity on A. In this situation, A is called a retract of B, which is thus a natural generalisation of the notion of an isomorphism, while both these notions are refinements of the concept of logical equivalence in operational terms, that is, in terms of computable functions.

It is interesting to note that the very first papers related to isomorphism of types were written before the notion itself appeared. Their subjects were the study of equality of terms defined on numbers, the isomorphism of objects in certain categories and the invertibility of . The earliest publications related to this problem date from the 1940s, cf. Birkhoff (1940) – an extensive bibliography may be found in Burris and Yeats (2002).

The relation of inclusion between types has been suggested by the practice of programming as it enriches the polymorphism of functional languages. We propose a simple (and linear) sequent calculus for subtyping as logical entailment. This allows us to derive a complete and coherent approach to subtyping from a few, logically meaningful sequents. In particular, transitivity and anti-symmetry will be derived from elementary logical principles.

The relation of inclusion between types has been suggested by the practice of programming, as it enriches the polymorphism of functional languages. We propose a simple (and linear) calculus of sequents for subtyping as logical entailment. This allows to derive a complete and coherent approach to subtyping from a few, logically meaningful, sequents. In particular, transitivity and anti-symmetry are derived from elementary logical principles, which stresses the power of sequents and Gentzen-style proof methods. Indeed, proof techniques based on cut-elimination are at the core of our results.

In this work we show how some useful reductions known from ordinary intuitionistic propositional calculus can be modified for Intuitionistic Linear Logic (without modalities). The main reductions we consider are: (1) the reduction of the depth of formulas in the sequents by addition of new variables, and (2) the elimination of linear disjunction, tensor and constant F. Both transformations preserve deducibility, that is, a transformed sequent is deducible if and only if the initial one was deducible. The size of the sequent grows linearly in case (1) and ≤ On8 in case (2).

The authors focus on how polymorphic functions, which may take types as inputs, depend on types. These functions are generally understood to have an essentially constant meaning, in all models, on input types. It is shown how the proof theory of the polymorphic lambda -calculus suggests a clear syntactic description of this phenomenon. Under a reasonable condition, it is shown that identity of two polymorphic functions on a single type implies identity of the functions (equivalently, every type is a generic input).>