Both firstand second-order logic (FOL and SOL, respectively) as we use them today were arguably created by Frege in his Begriffsschrift – if we ignore the notational differences. SOL also suggests itself as a natural, and because of its much greater strength, desirable extension of FOL. But at least since W. V. Quine’s famous claim that SOL is “set theory in sheep’s clothing” it is widely held ...

The Ordered conjecture of Kolaitis and Vardi asks whether xed point logic di ers from rst order logic on every in nite class of nite ordered structures In this paper we develop the tool of bounded variable element types and illustrate its application to this and the orig inal conjectures of McColm which arose from the study of inductive de nability and in nitary logic on pro cient classes of ni...

Logic programming (LP) is often seen as a way to overcome several shortcomings of the Web Ontology Language (OWL), such as the inability to model integrity constraints or perform closed-world querying. However, the open-world semantics of OWL seems to be fundamentally incompatible with the closed-world semantics of LP. This has sparked a heated debate in the Semantic Web community, resulting in...

With the increasing number of users and emergence different types network services, a multi-server architecture has emerged in recent years. In order to ensure secure communication Internet participants an open environment, authentication key agreement protocol for architectures were proposed past. 2018, Chatterjee et al. put forward lightweight three-factor they claimed that all known security...

it is expected that the legislator should pass only clear and unambiguous laws. although the legislators do their best at codification and approving the laws, there would be some ambiguities while executing them and therefore they require some interpretation.interpretation of laws is a very difficult task and it requires a systematic and logic method and the judges and lawyers should not interp...

Lincoln, Scedrov and Shankar proved undecidability of intuitionistic second order multiplicative commutative linear logic by embedding LJ2 into this logic. Emms did the same for intuitionistic second order non-commutative linear logic. Recently, Lafont and Scedrov demonstrated undecidability of classical second order multiplicative commutative linear logic. As for classical second order non-com...

Polyadic Higher-Order Fixpoint Logic (PHFL) is a modal fixpoint logic obtained as the merger of Higher-Order Fixpoint Logic (HFL) and the Polyadic μ-Calculus. Polyadicity enables formulas to make assertions about tuples of states rather than states only. Like HFL, PHFL has the ability to formalise properties using higher-order functions. We consider PHFL in the setting of descriptive complexity...

In order to understand complex genetic regulatory networks researchers require automated formal modelling techniques that provide appropriate analysis tools. In this paper we propose a new qualitative model for genetic regulatory networks based on Petri nets and detail a process for automatically constructing these models using logic minimization. We take as our starting point the Boolean netwo...