First Order Logic

The use of mathematical methods in the development of software is essential when reliable systems are sought; in particular they are now strongly recommended by the official norms adopted in the production of critical software.

This textbook provides a self-contained introduction to decidability of first-order theories and their combination. The technical material is presented in a systematic and universal way and illustrated with plenty of examples and a range of proposed exercises.

This is the first comprehensive textbook on higher-order logic that is written specifically to introduce the subject matter to graduate students in philosophy. The book covers both the formal aspects of higher-order languages―their model theory and proof theory, the theory of λ-abstraction and its generalizations―and their philosophical applications, especially to the topics of modality and propositional granularity. The book has a strong focus on non-extensional higher-order logics, making it more appropriate for foundational metaphysics than other introductions to the subject from computer science, mathematics, and linguistics.

This is the first comprehensive textbook on higher-order logic that is written specifically to introduce the subject matter to graduate students in philosophy. The book covers both the formal aspects of higher-order languages―their model theory and proof theory, the theory of λ-abstraction and its generalizations―and their philosophical applications, especially to the topics of modality and propositional granularity. The book has a strong focus on non-extensional higher-order logics, making it more appropriate for foundational metaphysics than other introductions to the subject from computer science, mathematics, and linguistics.

Most subfields of computer science have an interface layer via which applications communicate with the infrastructure, and this is key to their success (e.g., the Internet in networking, the relational model in databases, etc.). So far this interface layer has been missing in AI. First-order logic and probabilistic graphical models each have some of the necessary features, but a viable interface layer requires combining both. Markov logic is a powerful new language that accomplishes this by attaching weights to first-order formulas and treating them as templates for features of Markov random fields. Most statistical models in wide use are special cases of Markov logic, and first-order logic is its infinite-weight limit.