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Forgetting variables from a propositional formula may increase its size. Introducing new variables is a way to shorten it. Both operations can be expressed in terms of common equivalence, a weakened version of equivalence. In turn, common…
Abductive forgetting is removing variables from a logical formula while maintaining its abductive explanations. It is carried in two alternative ways depending on its intended application. Both differ from the usual forgetting, which…
Logical forgetting is \np-complete even in the simple case of propositional Horn formulae, and may exponentially increase their size. A way to forget is to replace each variable to forget with the body of each clause whose head is the…
This paper uses possible-world semantics to model the changes that may occur in an agent's knowledge as she loses information. This builds on previous work in which the agent may forget the truth-value of an atomic proposition, to a more…
Four algorithms for propositional forgetting are compared. The first performs all possible resolutions and deletes the clauses containing a variable to forget. The second forgets a variable at time by resolving and then deleting all clauses…
Logical forgetting may take exponential time in general, but it does not when its input is a single-head propositional definite Horn formula. Single-head means that no variable is the head of multiple clauses. An algorithm to make a formula…
Forgetting - or variable elimination - is an operation that allows the removal, from a knowledge base, of middle variables no longer deemed relevant. In recent years, many different approaches for forgetting in Answer Set Programming have…
Distilling from a knowledge base only the part that is relevant to a subset of alphabet, which is recognized as forgetting, has attracted extensive interests in AI community. In standard propositional logic, a general algorithm of…
Dependence is an important concept for many tasks in artificial intelligence. A task can be executed more efficiently by discarding something independent from the task. In this paper, we propose two novel notions of dependence in…
Solutions of symbolic regression problems are expressions that are composed of input variables and operators from a finite set of function symbols. One measure for evaluating symbolic regression algorithms is their ability to recover…
Independence -- the study of what is relevant to a given problem of reasoning -- has received an increasing attention from the AI community. In this paper, we consider two basic forms of independence, namely, a syntactic one and a semantic…
Forgetting a belief acquisition episode may not cause information loss because of the others. Checking whether it does is not obvious, as the contribution of each belief revision is not isolated from the others, and the same information may…
Memory and forgetting constitute two sides of the same coin, and although the first has been rigorously investigated, the latter is often overlooked. A number of experiments under the realm of psychology and experimental neuroscience have…
In combinatorics on words, a word $w$ over an alphabet $\Sigma$ is said to avoid a pattern $p$ over an alphabet $\Delta$ of variables if there is no factor $f$ of $w$ such that $f=h(p)$ where $h:\Delta^*\to\Sigma^*$ is a non-erasing…
Models trained on a new task typically degrade on prior tasks, a phenomenon known as forgetting. Traditionally, mitigating forgetting has required replaying stored exemplars from prior tasks, which is often impractical. By contrast,…
Forgetting a specific belief revision episode may not erase information because the other revisions may provide or entail the same information. Whether it does was proved coNP-hard for sequences of two arbitrary lexicographic revisions or…
Among the myriad of desirable properties discussed in the context of forgetting in Answer Set Programming (ASP), strong persistence naturally captures its essence. Recently, it has been shown that it is not always possible to forget a set…
In this paper we investigate forgetting in disjunctive logic programs, where forgetting an atom from a program amounts to a reduction in the signature of that program. The goal is to provide an approach that is syntax-independent, in that…
Forgetting as a knowledge management operation deliberately ignores parts of the knowledge and beliefs of an agent, for various reasons. Forgetting has many facets, one may want to forget parts of the syntax, a proposition, or a…
The problem of guessing a random string is revisited. A close relation between guessing and compression is first established. Then it is shown that if the sequence of distributions of the information spectrum satisfies the large deviation…