Restricted Unification in the DL FL₀: Extended Version

Unification in the Description Logic (DL) FL₀ is known to be ExpTimecomplete, and of unification type zero. We investigate in this paper whether a lower complexity of the unification problem can be achieved by either syntactically restricting the role depth of concepts or semantically restricting the length of role paths in interpretations. We show that the answer to this question depends on whether the number formulating such a restriction is encoded in unary or binary: for unary coding, the complexity drops from ExpTime to PSpace. As an auxiliary result, which is however also of interest in its own right, we prove a PSpace-completeness result for a depth-restricted version of the intersection emptiness problem for deterministic root-to-frontier tree automata. Finally, we show that the unification type of FL₀ improves from type zero to unitary (finitary) for unification without (with) constants in the restricted setting

A study on unification and disunification modulo

Dissertação (mestrado)—Universidade de Brasília, Instituto de Ciências Exatas, Departamento de Ciência da Computação, 2020.Estuda-se a comparação entre unificação assimétrica e desunificação módulo teorias equa- cionais em relação às suas complexidades, como desenvolvida por Ravishankar, Narendran e Gero. A unificação assimétrica é um tipo de unificação equacional em que as soluções devem fornecer o lado direito dos problemas apresentados na forma normal. E a desunifi- cação é resolver problemas com equações e “disequações” em relação à uma teoria equaci- onal dada. As soluções para os problemas de desunificação são substituições que tornam os dois termos de cada equação iguais, mas os dois termos de cada “disequação” diferen- tes. Unificação e desunificação equacional foram comparadas por os autores mencionados com relação as suas complexidades de tempo para duas teorias equacionais: a primeira associativa (A), comutativa (C), com unidade (U) e nilpotente (N), como (ACUN) e a segunda com tais propriedades, mas adicionando um homomorfismo (h), como (ACUNh), mostrando que desunificação pode ser resolvida em tempo polinomial enquanto unificação assimétrica é NP-difícil para ambas as teorias equacionais. Além disso, foi estudada a abordagem introduzidas por Zhiqiang Liu, em sua dissertação de doutorado, para converter osunificadores módulo ACUN em assimétricos, com símbolos de função não interpretados, usando as regras de inferência. Para a teoria associativa comutativa com homomorfismo (ACh), estudou-se a prova de que unificação módulo ACh é indecidível, assim como o algoritmo de semi-decisão, recentemente introduzido por Ajay Kumar Eeralla e Christopher Lynch, que apresenta um conjunto de regras de inferência para resolver o problema com limitações.Comparisons between asymmetric unification and disunification modulo AC concerning their complexities, as developed by Ravishankar, Narendran and Gero are studied. Asym- metric unification is a type of equational unification problem in which the solutions must give as right-hand sides of the input problem, normal forms regarding some rewriting sys- tem. And disunification problems require solving equations and "disequations" for a given equational theory. Solutions to the disunification problems are substitutions that make the two terms of each equation equal, but the two terms of each “disequation” different. These authors compared the complexity of the unification and disunification problems for two equational theories. The properties of the first equational theory are associativity (A), commutativity (C), the existence of unity (U), and nilpotence (N), abbreviated as ACUN. And, the second equational theory has the same properties but adds a homomorphism (h), for short, ACUNh. For such equational theories, details of the proof that disunification can be solved in polynomial time while the asymmetric unification is NP-hard have been studied. Besides, the approach for converting ACUN unifiers to asymmetric ones, with uninterpreted function symbols using the inference rules introduced by Zhiqiang Liu, in his Ph.D. dissertation, was studied. Narendran’s proof of the undecidability of the unifi- cation problem modulo the associative commutative theory with homomorphism ACh is studied. Also, the semi-decision algorithm, recently introduced by Ajay Kumar Eeralla and Christopher Lynch, is studied, which presents a set of inference rules for solving a bounded version of ACh unification

CP-violating Z-gamma-gamma and top-quark electric dipole couplings in gamma gamma -> t bar{t}

An effective anomalous CP-violating Z-gamma-gamma coupling can give rise to observable CP-odd effects in gamma gamma -> t bar{t}. We study certain asymmetries in the decay lepton distributions in gamma gamma -> t bar{t} arising from top decay in the presence of a CP-violating Z-gamma-gamma coupling as well as a top-quark electric dipole coupling. We find that a photon linear collider with geometric luminosity of 20 fb^{-1} can put limits of the order of 0.1 on the imaginary part of the CP-violating anomalous Z-gamma-gamma coupling using these asymmetries.Comment: 10 pages, latex, two figures included, Version accepted for publication in PL

CP-violating Zγγ and top-quark electric dipole couplings in γγ→tt̅

An effective anomalous CP-violating Zγγ coupling can give rise to observable CP-odd effects in γγ→tt̅. We study certain asymmetries in the decay lepton distributions in γγ→tt̅ arising from top decay in the presence of a CP-violating Zγγ coupling as well as a top-quark electric dipole coupling. We find that a photon linear collider with geometric luminosity of 20 fb−1 can put limits of the order of 0.1 on the imaginary part of the CP-violating anomalous Zγγ coupling using these asymmetries

Compartmentalized Connection Graphs for Concurrent Logic Programming II : Parallelism, Indexing and Unification

This report continues to document the development of a logic programming paradigm with implicit control, based in a compartmentalized connection graph theorem prover. Whilst the research has as it main goal the development of a language in which programs can be written with much less explicit control than PROLOG and its existing successors, a secondary goal is to exploit the immense parallelism inherent in the connection graph. The focus of this paper is the documentation of the extent of the parallelism inherent in the proof procedure. We characterize six different forms of parallelism These various forms of parallelism can be further classified into two classes: those associated with the performance of resolution steps, and those which are more concerned with unification. Unification is thus also a major topic of this report. In the first report of this series unification was identified as a major source of the cost of executing a logic program, or of proving a theorem. It turns out that deferring unification is the one of the best ways of dealing with it: hashing to perform it, and indexing to avoid it. Indexing and hashing, therefore, is the third topic covered in this report