Related papers: Relativized Propositional Calculus
We define the concept of a logic frame, which extends the concept of an abstract logic by adding the concept of a syntax and an axiom system. In a recursive logic frame the syntax and the set of axioms are recursively coded. A recursive…
This paper describes a method used to construct infinitely many probable counterexamples of the abc conjecture over the rational integers.
The remarkable success of Artificial Intelligence in advancing automated decision-making is evident both in academia and industry. Within the plethora of applications, ranking systems hold significant importance in various domains. This…
We introduce deterministic concurrent systems as a subclass of concurrent systems. Deterministic concurrent system are "locally commutative" concurrent systems. We prove that irreducible and deterministic concurrent systems have a unique…
We survey a collective achievement of a group of researchers: the PCP Theorems. They give new definitions of the class \np, and imply that computing approximate solutions to many \np-hard problems is itself \np-hard. Techniques developed to…
In this article, the decidability and computability issues of dynamic probability logic (DPL) are addressed. Firstly, a proof system $\mathcal{H}_{DPL}$ is introduced for DPL and shown that it is weakly complete. Furthermore, this logic has…
In answer set programming, two groups of rules are considered strongly equivalent if they have the same meaning in any context. Strong equivalence of two programs can be sometimes established by deriving rules of each program from rules of…
A measure of complexity based on a probabilistic description of physical systems is proposed. This measure incorporates the main features of the intuitive notion of such a magnitude. It can be applied to many physical situations and to…
Within the framework of computable infinitary continuous logic, we develop a system of hyperarithmetic numerals. These numerals are infinitary sentences in a metric language $L$ that have the same truth value in every interpretation of $L$.…
Properties such as provable security and correctness for randomized programs are naturally expressed relationally as approximate equivalences. As a result, a number of relational program logics have been developed to reason about such…
A diagrammatic logical calculus for the syllogistic reasoning is introduced and discussed. We prove that a syllogism is valid if and only if it is provable in the calculus.
Teaching proofs is a crucial component of any undergraduate-level program that covers formal reasoning. We have developed a calculational reasoning format and refined it over several years of teaching a freshman-level course, "Logic and…
We develop a semantics for logics of imperfect information with respect to general models. Then we build a proof system and prove its soundness and completeness with respect to this semantics.
We present a~novel approach to the problem of automated theorem proving. Polynomial cost procedures that recognise sentences belonging to a theory are generated on a basis of a set of axioms of the so-called Truncated Predicate Calculus…
Counting propositional logic was recently introduced in relation to randomized computation and shown able to logically characterize the full counting hierarchy. In this paper we aim to clarify the intuitive meaning and expressive power of…
In this paper we present a tableau proof system for first order logic of proofs FOLP. We show that the tableau system is sound and complete with respect to Mkrtychev models of FOLP.
Procedural computer languages have long been used in many aspects of mathematics pedagogy. In this work, we examine the use of Prolog, a declarative language for the same purpose. We find the facts+rules aspect of Prolog to be a novel…
The wide application of estimation techniques in system analysis enable us to best determine and understand the history of system states. This paper attempts to delineate the theory behind linear and non-linear estimation with a suitable…
The PCP Theorem is one of the most stunning results in computational complexity theory, a culmination of a series of results regarding proof checking it exposes some deep structure of computational problems. As a surprising side-effect, it…
This paper discusses a method for implementing a probabilistic inference system based on an extended relational data model. This model provides a unified approach for a variety of applications such as dynamic programming, solving sparse…