Related papers: Structural Completeness in bi-IPC
Temporal logic is a very powerful formalism deeply investigated and used in formal system design and verification. Its application usually reduces to solving specific decision problems such as model checking and satisfiability. In these…
We introduce and develop a topological semantics of conservativity logics and interpretability logics. We prove the topological compactness theorem of consistent normal extensions of the conservativity logic $\mathbf{CL}$ by extending…
This paper investigates the logical strength of completeness theorems for modal propositional logic within second-order arithmetic. We demonstrate that the weak completeness theorem for modal propositional logic is provable in…
Rewriting logic is naturally concurrent: several subterms of the state term can be rewritten simultaneously. But state terms are global, which makes compositionality difficult to achieve. Compositionality here means being able to decompose…
It is known that the set of tautologies of second order intuitionistic propositional logic, $\mathrm{IPC} 2$, is undecidable. Here, we prove that the sets of formulas of $\mathrm{IPC} 2$ which are true in the algebra of open subsets of…
This paper surveys main and recent studies on temporal logics in a broad sense by presenting various logic systems, dealing with various time structures, and discussing important features, such as decidability (or undecidability) results,…
I deal with two approaches to proof-theoretic semantics: one based on argument structures and justifications, which I call reducibility semantics, and one based on consequence among (sets of) formulas over atomic bases, called base…
Cirquent calculus is a proof system with inherent ability to account for sharing subcomponents in logical expressions. Within its framework, this article constructs an axiomatization CL18 of the basic propositional fragment of computability…
We advocate here the use of computational logic for systems biology, as a \emph{unified and safe} framework well suited for both modeling the dynamic behaviour of biological systems, expressing properties of them, and verifying these…
The paper gives a soundness and completeness proof for the implicative fragment of intuitionistic calculus with respect to the semantics of computability logic, which understands intuitionistic implication as interactive algorithmic…
Over the last two decades, there has been an extensive study on logical formalisms for specifying and verifying real-time systems. Temporal logics have been an important research subject within this direction. Although numerous logics have…
In the same sense as classical logic is a formal theory of truth, the recently initiated approach called computability logic is a formal theory of computability. It understands (interactive) computational problems as games played by a…
We first partly develop a mathematical notion of stable consistency intended to reflect the actual consistency property of human beings. Then we give a generalization of the first and second G\"odel incompleteness theorem to stably…
In [17], we introduced a modal logic, called $L$, which combines intuitionistic propositional logic $IPC$ and classical propositional logic $CPC$ and is complete w.r.t. an algebraic semantics. However, $L$ seems to be too weak for…
We prove undecidability and pinpoint the place in the arithmetical hierarchy for commutative action logic, that is, the equational theory of commutative residuated Kleene lattices (action lattices), and infinitary commutative action logic,…
In this paper we present a constructive proof of cut elimination for a system of full second order logic with the structural rules absorbed and using sets instead of sequences. The standard problem of the cutrank growth is avoided by using…
We investigate the complexity of the model checking problem for intuitionistic and modal propositional logics over transitive Kripke models. More specific, we consider intuitionistic logic IPC, basic propositional logic BPL, formal…
A thorough investigation of the foundations of paraconsistent logics. Relations between logical principles are formally studied, a novel notion of consistency is introduced, the logics of formal inconsistency, and the subclasses of…
This paper proposes an alternative to standard first-order logic that seeks greater naturalness, generality, and semantic self-containment. The system removes the first-order restriction, avoids type hierarchies, and dispenses with external…
The characterizing properties of a proof-theoretical presentation of a given logic may hang on the choice of proof formalism, on the shape of the logical rules and of the sequents manipulated by a given proof system, on the underlying…