Let `c and `i denote derivability in classical and intuitionistic propositional logic, respectively. Then it is known that if `c A, then ΠV(A) `i A, where V(A) is the set of propositional variables in a formula A and ΠV = {p ∨ ¬p | p ∈ V } for a set V of propositional variables; see, for example, [1], and [4, p. 27] which was originally given in [5]. In this talk, we consider a problem: what se...

We study the finite satisfiability problem for first order logic with two variables and two binary relations, corresponding to the induced successor relations of two finite linear orders. We show that the problem is decidable in NExpTime.

Tarskian semantics is called "Tarskian" for historical reasons (Tarski, 1936). A more descriptive name would be "systematic denotational semantics," or SD for short. The method is called "denotational" because it specified the meanings of a notation in terms of what its expressions denote. The method is called "systematic" in hopes that the rules that assign meaning are precise enough to suppor...

The F-bounding condition is de ned by Canning et al. [Canning 89] as t F [t], where is the subtyping relation and F [t] is an expression, generally containing the type variable t. Because Canning's work is proof theoretic, this essentially syntactic de nition is natural. In our technical report \Typechecking Polymorphism in Emerald", Hutchinson and I de ne the relation . (read matches) used to ...

Analogues of the classical omitting types theorems of first-order logic are proved for propositional logic. For an infinite cardinal κ, a sufficient criterion is given for the omission of κ-many types in a propositional language with κ propositional variables.

Reasoning about time and space is essential for many applications, especially for robots and other autonomous systems that act in the real world and need to reason about it. In this paper we present a pragmatic approach to spatio-temporal stream reasoning integrated in the Robot Operating System through the DyKnow framework. The temporal reasoning is done in the Metric Temporal Logic and the sp...

The composition of logic programs out of clauses has been studied semantically, but not the composition of a single clause out of its components. Structurally, a logic program can be regarded as a sentence in clausal form. In his procedural interpretation of logic programs, Kowalski has shown that a positive Horn clause can be viewed as a procedure in the programming sense. This interpretation ...

Given a statistical model for the request frequencies and sizes of data objects in a caching system, we derive the probability density of the size of the file that accounts for the largest amount of data traffic. This is equivalent to finding the required size of the cache for a caching placement that maximizes the expected byte hit ratio for given file size and popularity distributions. The fi...