We propose a novel formalism, calledFrame Logic(abbr., F-logic), that accounts in a clean and declarative fashion for most of the structural aspects of object-oriented and frame-based languages. These features include object identity, complex objects, inheritance, polymorphic types, query methods, encapsulation, and others. In a sense, F-logic stands in the same relationship to the object-oriented paradigm as classical predicate calculus stands to relational programming. F-logic has a model-theoretic semantics and a sound and complete resolution-based proof theory. A small number of fundamental concepts that come from object-oriented programming have direct representation in F-logic; other, secondary aspects of this paradigm are easily modeled as well. The paper also discusses semantic issues pertaining to programming with a deductive object-oriented language based on a subset of F-logic.

A logic called typed predicate calculus (TPC) that gives declarative meaning to logic programs with type declarations and type inference is introduced. The proper interaction between parametric and inclusion varieties of polymorphism is achieved through a construct called type dependency, which is analogous to implication types but yields more natural and succinct specifications. Unlike other proposals where typing has extra-logical status, in TPC the notion of type-correctness has precise model-theoretic meaning that is independent of any specific type-checking or type-inference procedure. Moreover, many different approaches to typing that were proposed in the past can be studied and compared within the framework of TPC. Another novel feature of TPC is its reflexivity with respect to type declarations; in TPC, these declarations can be queried the same way as any other data. Type reflexivity is useful for browsing knowledge bases and, potentially, for debugging logic programs.>

We present a logic for reasoning about complex objects, which is a revised and significantly extended version of Maier's O-logic [Mai86]. The logic naturally supports complex objects, object identity, deduction, is tolerant to inconsistent data, and has many other interesting features. It elegantly combines the object-oriented and value-oriented paradigms and, in particular, contains all of the predicate calculus as a special case. Our treatment of sets is also noteworthy: it is more general than ELPS [Kup87] and COL [AbG87], yet it avoids the semantic problems encountered in LDL [BNS87]. The proposed logic has a sound and complete resolution-based proof procedure.