Vasilyi Shangin

Natural deduction calculus for linear-time temporal logic

We present a natural deduction calculus for the propositional linear-time temporal logic and prove its correctness. The system extends the natural deduction construction of the classical propositional logic. This will open the prospect to apply our technique as an automatic reasoning tool in a deliberative decision making framework across various AI applications.

Socratic Proofs for Quantifiers

First-order logic is formalized by means of tools taken from the logic of questions. A calculus of questions which is a counterpart of the Pure Calculus of Quantifiers is presented. A direct proof of completeness of the calculus is given.

Natural Deduction Calculus for Computation Tree Logic

The authors present a natural deduction calculus for the computation tree logic, CTL, defined with the full set of classical and temporal logic operators. The system extends the natural deduction construction of the linear-time temporal logic. This opens the prospect to apply our technique as an automatic reasoning tool in a deliberative decision making framework across various applications in AI and computer science, where the branching-time setting is required

Automated Natural Deduction for Propositional Linear-Time Temporal Logic

We present a proof searching technique for the natural deduction calculus for the prepositional linear-time temporal logic and prove its correctness. This opens the prospect to apply our technique as an automated reasoning tool in a number of emerging computer science applications and in a deliberative decision making framework across various AI applications.

Tackling Incomplete System Specifications Using Natural Deduction in the Paracomplete Setting

In many modern computer applications the significance of specification based verification is well accepted. However, when we deal with such complex processes as the integration of heterogeneous systems, parts of specification may be not known. Therefore it is important to have techniques that are able to cope with such incomplete information. An adequate formal setup is given by so called Para complete logics, where, contrary to the classical framework, for some statements we do not have evidence to conclude if they are true or false. As a consequence, for example, the law of excluded middle is not valid. In this paper we justify how the automated proof search technique for Para complete logic PComp can be efficiently applied to the reasoning about systems with incomplete information. Note that for many researchers, one of the core features of natural deduction, the opportunity to introduce arbitrary formulae as assumptions, has been a point of great scepticism regarding thievery possibility of the automation of the proof search. Here, not only we show the contrary, but we also turned the assumptions management into an advantage showing the applicability of the proposed technique to assume-guarantee reasoning.