Most introductory courses on logic teach only the syntax of first-order predicate calculus and give a few simple proofs, usually of theorems in arithmetic. Advanced courses are taught in mathematics departments, where they lead to topics that have little or no application to linguistics. In one of the standard textbooks, Schoenfield (1967) explicitly states "Mathemat ical logic has always been ...

In this paper, we provide a semantic study of the first-order predicate logic for situations involving uncertainty. We introduce the concepts of uncertain predicate proposition, uncertain predicate formula, uncertain interpretation and degree of truth in the framework of uncertainty theory. Compared with classical predicate formula taking true value in {0, 1}, the degree of truth of uncertain p...

We describe a new problem solver called STRIPS that attempts to find a sequence o f operators in a spcce o f world models to transform a given initial world model into a model in which a given goal formula can be proven to be true. STRIPS represents a world n,~del as an arbitrary collection o f first-order predicate calculus formulas and is designed to work with .models consisting o f large num...

Knowledge based artificial neural networks have been applied quite successfully to propositional knowledge representation and reasoning tasks. However, as soon as these tasks are extended to structured objects and structure-sensitive processes as expressed e.g., by means of first-order predicate logic, it is not obvious at all what neural symbolic systems would look like such that they are trul...

We define a sound and complete logic, called FO⊃, which extends classical first-order predicate logic with intuitionistic implication. As expected, to allow the interpretation of intuitionistic implication, the semantics of FO⊃ is based on structures over a partially ordered set of worlds. In these structures, classical quantifiers and connectives (in particular, implication) are interpreted wi...

Tarski-Givant’s map calculus is briefly reviewed, and a plan of research is outlined aimed at investigating applications of this ground equational formalism in the theorem-proving field. The main goal is to create synergy between first-order predicate calculus and the map calculus. Techniques for translating isolated sentences, as well as entire theories, from first-order logic into map calculu...

In Wason's selection task, subjects see four cards showing symbols like E, K, 4, and 7, and are told that each card has a letter on one side and a number on the other. The task is to choose the cards that need to be turned over in order to determine whether the following rule is true or false: “If a card has a vowel on one side, then it has an even number on the other side.” Most subjects choos...

It is well-known that there exist consistent first-order theories that become inconsistent when we add Tarski’s schema T. This is Tarski’s Theorem. To avoid the inconsistency result, one can restrict Tarski’s schema in different ways. In our paper we restrict Tarski’s schema T by only instantiating the schema with a proper subset of the set of all sentences. We prove several results concerning ...

Lambda abstraction algebras (LAAs) are designed to algebraize the untyped lambda calculus in the same way cylindric and polyadic algebras algebraize the first-order predicate logic. Like combinatory algebras they can be defined by true identities and thus form a variety in the sense of universal algebra, but they differ from combinatory algebras in several important respects. The most natural L...

In this paper, we develop the algorithm, given in Plotkin (1970), for finding the least generalization of two clauses, into a theory of inductive generalization. The types of hypothesis which can be formed are very simple. They all have the form: (x)Pxm Qx. We have been guided by ideas from the philosophy of science, following Buchanan (1966). There is no search for infallible methods of genera...