Related papers: Generalization of Clauses under Implication
The main operations in Inductive Logic Programming (ILP) are generalization and specialization, which only make sense in a generality order. In ILP, the three most important generality orders are subsumption, implication and implication…
Recent breakthroughs in AI have shown the remarkable power of deep learning and deep reinforcement learning. These developments, however, have been tied to specific tasks, and progress in out-of-distribution generalization has been limited.…
According to the principle of compositional generalization, the meaning of a complex expression can be understood as a function of the meaning of its parts and of how they are combined. This principle is crucial for human language…
Tsetlin Machines (TMs) have garnered increasing interest for their ability to learn concepts via propositional formulas and their proven efficiency across various application domains. Despite this, the convergence proof for the TMs,…
Generic programming (GP) is an increasingly important trend in programming languages. Well-known GP mechanisms, such as type classes and the C++0x concepts proposal, usually combine two features: 1) a special type of interfaces; and 2)…
The goal of this paper is to extend classical logic with a generalized notion of inductive definition supporting positive and negative induction, to investigate the properties of this logic, its relationships to other logics in the area of…
The definition is a common form of human expert knowledge, a building block of formal science and mathematics, a foundation for database theory and is supported in various forms in many knowledge representation and formal specification…
A standard form of analysis for linguistic typology is the universal implication. These implications state facts about the range of extant languages, such as ``if objects come after verbs, then adjectives come after nouns.'' Such…
The ability to learn and act in novel situations is still a prerogative of animate intelligence, as current machine learning methods mostly fail when moving beyond the standard i.i.d. setting. What is the reason for this discrepancy? Most…
It is commonly agreed that the success of future proof assistants will rely on their ability to incorporate computations within deduction in order to mimic the mathematician when replacing the proof of a proposition P by the proof of an…
The clausal logical consequences of a formula are called its implicates. The generation of these implicates has several applications, such as the identification of missing hypotheses in a logical specification. We present a procedure that…
The Tsetlin Machine (TM) is a machine learning algorithm founded on the classical Tsetlin Automaton (TA) and game theory. It further leverages frequent pattern mining and resource allocation principles to extract common patterns in the…
The usual reading of logical implication "A implies B" as "if A then B" fails in intuitionistic logic: there are formulas A and B such that "A implies B" is not provable, even though B is provable whenever A is provable. Intuitionistic…
A major difficulty in developing and maintaining very large knowledge bases originates from the variety of forms in which knowledge is made available to the KB builder. The objective of this research is to bring together two complementary…
After surveying classical results, we introduce a generalized notion of inference system to support structural recursion on non-well-founded data types. Besides axioms and inference rules with the usual meaning, a generalized inference…
Description logics (DL) are a family of formal languages for representing and reasoning about structured knowledge in terms of concepts and their relationships. A central reasoning problem in DL is concept subsumption. Although this problem…
Prime implicates and prime implicants have proven relevant to a number of areas of artificial intelligence, most notably abductive reasoning and knowledge compilation. The purpose of this paper is to examine how these notions might be…
Description logics (DLs) are standard knowledge representation languages for modelling ontologies, i.e. knowledge about concepts and the relations between them. Unfortunately, DL ontologies are difficult to learn from data and…
We consider problems of making sequences of decisions to accomplish tasks, interacting via the medium of language. These problems are often tackled with reinforcement learning approaches. We find that these models do not generalize well…
Large language models (LLMs) exhibit remarkable task generalization, solving tasks they were never explicitly trained on with only a few demonstrations. This raises a fundamental question: When can learning from a small set of tasks…