Unital Anti-Unification: Type and Algorithms

Unital equational theories are defined by axioms that assert the existence of the unit element for some function symbols. We study anti-unification (AU) in unital theories and address the problems of establishing generalization type and designing anti-unification algorithms. First, we prove that when the term signature contains at least two unital functions, anti-unification is of the nullary type by showing that there exists an AU problem, which does not have a minimal complete set of generalizations. Next, we consider two special cases: the linear variant and the fragment with only one unital symbol, and design AU algorithms for them. The algorithms are terminating, sound, complete, and return tree grammars from which the set of generalizations can be constructed. Anti-unification for both special cases is finitary. Further, the algorithm for the one-unital fragment is extended to the unrestricted case. It terminates and returns a tree grammar which produces an infinite set of generalizations. At the end, we discuss how the nullary type of unital anti-unification might affect the anti-unification problem in some combined theories, and list some open questions

COLLECTIVE TRAUMA IN REFUGEE LITERATURE (BASED ON ALMANACS – 14 GIGABYTES AND HALLELUIAH)

Theories of traumatic memory are uniquely topical in modern theoretical discourse, Collective trauma is a complex of psychological sensations, which is formed in witnesses or participants of tragic events, who have to deal with psychological stigma. Theoretical framework about the collective trauma is relevant to events that have taken place in Georgia, as the epochal tragedy has changed ethnic and cultural environment in Abkhazia and Tskhinvali Region. As the subject of research, we have defined the almanacs reflecting Georgian-Abkhazian and Georgian-Ossetian (provoked by the third force) conflicts: 14 Gigabytes and Halleluiah. Uniqueness of 14 Gigabytes is reasoned by the concept set by the editor (Nana Gaprindashvili) and the complier of the almanac (Tea Kalandia) – 14 narrators tell about the Abkhazian episode of Russian-Georgian war. Personal stories create the monumental canvas-reflection of the feelings of youth who have been deprived of childhood. Authors of the poetic almanac Halleluiah published in 2018, under the editorship of Mzia Khetaguri, are united under refugee stigma, pain caused by losing homes, trauma, which marks each of the texts like an unhealed wound. It must be emphasized that in none of the researched authors’ texts reflects hostility or aggression towards “conflicting sides” or even the main provoking power – Russia. The presented discourse allows us to confirm the research hypothesis: conflicts provoked by Russia have forced Georgian population of Abkhazia and Tskhinvali Region to leave their homes, to go through the horrors of war. Refugees have to deal with the stigma of being refugees and grave experience of collective trauma, which is creatively transformed, reflexed in the almanacs 14 Gigabytes and Halleluiah.Theories of traumatic memory are uniquely topical in modern theoretical discourse, Collective trauma is a complex of psychological sensations, which is formed in witnesses or participants of tragic events, who have to deal with psychological stigma. Theoretical framework about the collective trauma is relevant to events that have taken place in Georgia, as the epochal tragedy has changed ethnic and cultural environment in Abkhazia and Tskhinvali Region. As the subject of research, we have defined the almanacs reflecting Georgian-Abkhazian and Georgian-Ossetian (provoked by the third force) conflicts: 14 Gigabytes and Halleluiah. Uniqueness of 14 Gigabytes is reasoned by the concept set by the editor (Nana Gaprindashvili) and the complier of the almanac (Tea Kalandia) – 14 narrators tell about the Abkhazian episode of Russian-Georgian war. Personal stories create the monumental canvas-reflection of the feelings of youth who have been deprived of childhood. Authors of the poetic almanac Halleluiah published in 2018, under the editorship of Mzia Khetaguri, are united under refugee stigma, pain caused by losing homes, trauma, which marks each of the texts like an unhealed wound. It must be emphasized that in none of the researched authors’ texts reflects hostility or aggression towards “conflicting sides” or even the main provoking power – Russia. The presented discourse allows us to confirm the research hypothesis: conflicts provoked by Russia have forced Georgian population of Abkhazia and Tskhinvali Region to leave their homes, to go through the horrors of war. Refugees have to deal with the stigma of being refugees and grave experience of collective trauma, which is creatively transformed, reflexed in the almanacs 14 Gigabytes and Halleluiah

Order-Sorted Unification with Regular Expression Sorts

We extend first-order order-sorted unification by permitting regular expression sorts for variables and in the domains of function symbols. The set of basic sorts is finite. The obtained signature corresponds to a finite bottom-up hedge automaton. The unification problem in such a theory generalizes some known unification problems. Its unification type is infinitary. We give a complete unification procedure and prove decidability

Higher-Order Equational Pattern Anti-Unification

We consider anti-unification for simply typed lambda terms in associative, commutative, and associative-commutative theories and develop a sound and complete algorithm which takes two lambda terms and computes their generalizations in the form of higher-order patterns. The problem is finitary: the minimal complete set of generalizations contains finitely many elements. We define the notion of optimal solution and investigate special fragments of the problem for which the optimal solution can be computed in linear or polynomial time

A Generic Framework for Higher-Order Generalizations

We consider a generic framework for anti-unification of simply typed lambda terms. It helps to compute generalizations which contain maximally common top part of the input expressions, without nesting generalization variables. The rules of the corresponding anti-unification algorithm are formulated, and their soundness and termination are proved. The algorithm depends on a parameter which decides how to choose terms under generalization variables. Changing the particular values of the parameter, we obtained four new unitary variants of higher-order anti-unification and also showed how the already known pattern generalization fits into the schema

Anti-unification and Generalization: A Survey

Anti-unification (AU), also known as generalization, is a fundamental operation used for inductive inference and is the dual operation to unification, an operation at the foundation of theorem proving. Interest in AU from the AI and related communities is growing, but without a systematic study of the concept, nor surveys of existing work, investigations7 often resort to developing application-specific methods that may be covered by existing approaches. We provide the first survey of AU research and its applications, together with a general framework for categorizing existing and future developments.Comment: Accepted at IJCAI 2023 - Survey Trac

Learning and Generalisation in Neural Networks with Local Preprocessing

We study learning and generalisation ability of a specific two-layer feed-forward neural network and compare its properties to that of a simple perceptron. The input patterns are mapped nonlinearly onto a hidden layer, much larger than the input layer, and this mapping is either fixed or may result from an unsupervised learning process. Such preprocessing of initially uncorrelated random patterns results in the correlated patterns in the hidden layer. The hidden-to-output mapping of the network is performed by a simple perceptron, trained using a supervised learning process. We investigate the effects of the correlations on the learning and generalisation properties as opposed to those of a simple perceptron with uncorrelated patterns. As it turns out, this architecture has some advantages over a simple perceptron