It is widely recognized that equational logic is simple, (relatively) decidable, and (relatively) easily mechanized. But it is also widely thought that equational logic has limited applicability because it cannot handle subtypes or partial functions. We show that a modest stretch of equational logic eeectively handles these features. Space limits preclude a full theoretical treatment, so we oft...

Concept learning is the induction of a description from a set of examples. Inductive logic programming can be considered a special case of the general notion of concept learning specifically referring to the induction of first-order theories. Both concept learning and inductive logic programming can be seen as a search over all possible sentences in some representation language for sentences th...

We define abstract derivations for equational logic and use them to prove the interpolation property.

Concept learning is a branch of machine learning concerned with learning how to discriminate and categorize things based on positive and negative examples. More specifically, the learning algorithm induces a description of the concept (in some representation language) from a set of positive and negative facts. Inductive logic programming can be considered a subcategory of concept learning where...

The paper provides an organisation of order-sorted equational logic as an Institution.

We analyse the relationship between nominal algebra and nominal rewriting, giving a new and concise presentation of equational deduction in nominal theories. With some new results, we characterise a subclass of equational theories for which nominal rewriting provides a complete procedure to check nominal algebra equality. This subclass includes specifications of lambda-calculus and first-order ...

We present an approach for verifying dynamic systems specified in rewriting logic, a formal specification language implemented in the Maude system. Our approach is tailored for invariants, i.e., properties that hold on all states reachable from a given class of initial states. The approach consists in encoding invariance properties into inductive properties written in membership equational logi...

Concept learning is the induction of a description from a set of examples. Inductive logic programming can be considered a special case of the general notion of concept learning specifically referring to the induction of first-order theories. Both concept learning and inductive logic programming can be seen as a search over all possible sentences in some representation language for sentences th...

The ITP tool is an experimental inductive theorem prover for proving properties of Maude equational specifications, i.e., specifications in membership equational logic with an initial algebra semantics. The ITP tool has been written entirely in Maude and is in fact an executable specification of the formal inference system that it implements.