We show that there are continuum many different extensions of SCI (the basic theory of non-Fregean propositional logic) that lie below WF (the Fregean extension) and are closed under substitution. Moreover, continuum many of them are independent from WB (the Boolean extension), continuum many lie above WB and are independent from WH (the Boolean extension with only two values for the equality r...

We present the propositional fragment CLF0 of the Concurrent Logical Framework (CLF). CLF extends the Linear Logical Framework to allow the natural representation of concurrent computations in an object language. The underlying type theory uses monadic types to segregate values from computations. This separation leads to a tractable notion of definitional equality that identifies computations d...

We investigate a first-order conditional probability logic with equality, which is, up to our knowledge, the first treatise of such logic. The logic, denoted LFPOIC=, allows making statements such as: CP>s(φ, θ), and CP6s(φ, θ), with the intended meaning that the conditional probability of φ given θ is at least (at most) s. The corresponding syntax, semantic, and axiomatic system are introduced...

Many verification problems reduce to proving the validity of formulas involving both propositional connectives and domain-specific functions and predicates. This paper presents an explicating theorem prover architecture that leverages recent advances in propositional SAT solving and the development of proof-generating domain-specific procedures. We describe the implementation of an explicating ...