Start Date: 2023-03-17 End Date: 2026-03-17
Since the early days of Artificial Intelligence logical and probabilistic methods have been independently used in order to solve tasks that require some sorts of ``intelligence''. Probability theory deals with the challenges posed by uncertainty, while logic is more often used for reasoning with perfect knowledge. Considerable efforts have been devoted to combining logical and probabilistic methods in a single framework, which influenced the development of several formalisms and programming tools.
All probabilistic logic formalisms studied so far permit only individual variables, that can be instantiated by a single term. On the other hand, theories and systems that use also sequence variables (these variables can be replaced by arbitrary finite, possibly empty, sequences of terms) and unranked symbols (function and/or predicate symbols without fixed arity) have emerged. The unranked term is a first-order term, where the same function symbol can occur in different places with different number of arguments. Unranked function symbols and sequence variables bring a great deal of expressiveness in language.
The main novelty of the proposed project is to develop an unranked probabilistic logic, study its properties and introduce reasoning method for it. The novelty of our approach is that we will extend probabilistic logic with sequence variables and flexible-arity function and predicate symbols. To the best of our knowledge, such formalisms are not yet studied in the literature.
The project is interdisciplinary, since it combines the techniques from three scientific fields: mathematics (probability theory), logic (with sequence variables and terms) and computer science (automated reasoning methods). Such a combination is very common in modern artificial intelligence related projects. Not only the fundamental research proposed in the project is interdisciplinary, but the expected results of the project can be used in many other areas and in industry as well. The obtained formalism will have rich capabilities for various applications in e-shopping, randomized encryption, computational linguistics and the like.