Formal specification language and deduction system for object-oriented models is proposed in this article. It extends ς-calculus introduced by Martín Abadi and Luca Cardelli with propositional connectives, and quantified terms. The first-order type system of ς-calculus serves as typing theory of suggested calculus. Deduction system consists of reduction rules of ς-terms, equality theory of ς-ca...

Many applications of automated deduction require reasoning modulo background theories, in particular some form of integer arithmetic. Developing corresponding automated reasoning systems that are also able to deal with quantified formulas has recently been an active area of research. We contribute to this line of research and propose a novel instantiation-based method for a large fragment of fi...

The logic of equality with uninterpreted functions (EUF) has been proposed for verifying abstract hardware designs. Fast satisfiability checking over this logic is important for such verification to be successful. Our algorithm is based on the Davis-Putman-Logemann-Loveland (DPLL) procedure, one of the most effective methods to check propositional satisfiability. The DPLL procedure returns a sa...

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...