This talk is about a direction in logic which attempts to have something to say, and something to learn, from computational linguistics and natural language processing.

Much of modern logic originates in work on the foundations of mathematics. My talk reports on work in logic that has a different goal, the study of interference in language. This study leads to what I will call “natural logic,” the enterprise of studying logical interference in languages that look more like natural language than standard logical systems.

By now there is a growing body of work which presents logical systems that differ from first-order logic in various ways. Most of the systems are complete and decidable. Some are modern versions of syllogistic logic, but with additional features not present in syllogistic logics. And then there are flavors of logic which look rather far from ethical traditional or modern logic.

The talk will be programmatic and far-ranging rather than detailed. I hope to touch on computer implementations of natural logics, teaching materials on this topic, and interactions of logic and cognitive science.

Semantic Knowledge Base is a new approach towards building systems capable of storing and processing complex information also in the means of inference over it. The main assumption is to distinguish concepts (meanings) from terms (natural language identifiers). The information is held in two modules: ontological core and semantic network module. Ontological core is used for building a hypergraph, where each node is a concept and edges are links between them. Semantic networks are used to store more complex information (rules and facts) in a structure using predicate-object structures build over previously defined concepts. The system provides also support for inference in the means of modal and hybrid logic through custom build system of quantifiers and possibility of describing dimensions and spaces, where each and every part of information is valid or invalid (extended Kripke’s model of possible world theory).

The system has been designed in association oriented database model (AODB). In this model we assume two main categories: collections and associations. Collections are used to store information in objects holding the attributes values, while associations store information about n-ary relation between collections. Associations are consider to be containers for roles and each role is considered as the permission given to the collection to be part of an association. The model assumes that both, collections and association may build inheritance structures, where virtual, private and real inheritance of accordingly attributes and roles occur. Each of the structure elements of AODB has its own unique role therefore their semantic is strictly connected to the grammar of the model. Moreover such construction made it possible to unify conceptual and physical model of the database into one structure. AODB has its native object storage model. There have also been two languages designed and implemented – Association Modeling Language (AML) and Association Query Language (AQL). The latter is using graph templates as queries and returns list of graph.