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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…

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…

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…

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…

We present a recursive formulation of the Horn algorithm for deciding the satisfiability of propositional clauses. The usual presentations in imperative pseudo-code are informal and not suitable for simple proofs of its main properties. By…

Forgetting is removing variables from a logical formula while preserving the constraints on the other variables. In spite of being a form of reduction, it does not always decrease the size of the formula and may sometimes increase it. This…

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…

While previous researchers have performed an exhaustive search to determine an optimal Wordle strategy, that computation is very time consuming and produced a strategy using words that are unfamiliar to most people. With Wordle solutions…

We consider a class of formula equations in first-order logic, Horn formula equations, which are defined by a syntactic restriction on the occurrences of predicate variables. Horn formula equations play an important role in many…

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…

We consider constrained Horn clause solving from the more general point of view of solving formula equations. Constrained Horn clauses correspond to the subclass of Horn formula equations. We state and prove a fixed-point theorem for Horn…

This paper presents a new technique for optimizing formal analysis of propositional logic formulas and Linear Temporal Logic (LTL) formulas, namely the formula simplification table. A formula simplification table is a mathematical table…

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…

Our position is that logic programming is not programming in the Horn clause sublogic of classical logic, but programming in a logic of (inductive) definitions. Thus, the similarity between prototypical Prolog programs (e.g., member,…

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…

This paper proposes an alternative to standard first-order logic that seeks greater naturalness, generality, and semantic self-containment. The system removes the first-order restriction, avoids type hierarchies, and dispenses with external…

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…

We propose a novel framework seamlessly providing key properties of both neural nets (learning) and symbolic logic (knowledge and reasoning). Every neuron has a meaning as a component of a formula in a weighted real-valued logic, yielding a…

Multi-hop reading comprehension (RC) questions are challenging because they require reading and reasoning over multiple paragraphs. We argue that it can be difficult to construct large multi-hop RC datasets. For example, even highly…

We consider approximating data structures with collections of the items that they contain. For examples, lists, binary trees, tuples, etc, can be approximated by sets or multisets of the items within them. Such approximations can be used to…