Related papers: Many-valued coalgebraic dynamic logics: Safety and…
Dynamic reliability block diagrams (DRBDs) are introduced to overcome the modeling limitations of traditional reliability block diagrams, such as the inability to capture redundant components. However, so far there is no algebraic framework…
A variety of problems emerged investigating electronic circuits, computer devices and cellular automata motivated a number of attempts to create a differential and integral calculus for Boolean functions. In the present article, we extend…
Taking inspiration from the monadicity of complete atomic Boolean algebras, we prove that profinite modal algebras are monadic over Set. While analyzing the monadic functor, we recover the universal model construction - a construction…
Formal argumentation is being used increasingly in artificial intelligence as an effective and understandable way to model potentially conflicting pieces of information, called arguments, and identify so-called acceptable arguments…
We introduce a complete many-valued semantics for two normal lattice-based modal logics. This semantics is based on reflexive many-valued graphs. We discuss an interpretation and possible applications of this logical framework in the…
Any finite set of linear operators on an algebra $A$ yields an operator algebra $B$ and a module structure on A, whose endomorphism ring is isomorphic to a subring $A^B$ of certain invariant elements of $A$. We show that if $A$ is a…
We extend the meet-implication fragment of propositional intuitionistic logic with a meet-preserving modality. We give semantics based on semilattices and a duality result with a suitable notion of descriptive frame. As a consequence we…
A semantics for quantified modal logic is presented that is based on Kleene's notion of realizability. This semantics generalizes Flagg's 1985 construction of a model of a modal version of Church's Thesis and first-order arithmetic. While…
We obtain, for the first time, a modular many-valued semantics for combined logics, which is built directly from many-valued semantics for the logics being combined, by means of suitable universal operations over partial non-deterministic…
We propose a general framework to allow: (a) specifying the operational semantics of a programming language; and (b) stating and proving properties about program correctness. Our framework is based on a many-sorted system of hybrid modal…
This work presents a formalized proof of modal completeness for G\"odel-L\"ob provability logic (GL) in the HOL Light theorem prover. We describe the code we developed, and discuss some details of our implementation, focusing on our choices…
In this work, a novel quaternary algebra has been proposed that can be used to implement an arbitrary quaternary logic function in more than one systematic ways. The proposed logic has evolved from and is closely related to the Boolean…
This paper presents a many-sorted polyadic modal logic that generalizes some of the existing approaches. The algebraic semantics has led us to a many-sorted generalization of boolean algebras with operators, for which we prove the analogue…
Recursive definitions of predicates are usually interpreted either inductively or coinductively. Recently, a more powerful approach has been proposed, called flexible coinduction, to express a variety of intermediate interpretations,…
We prove completeness, interpolation, decidability and an omitting types theorem for certain multi dimensional modal logics where the states are not abstract entities but have an inner structure. The states will be sequences. Our approach…
We propose a graph-based extension of Boolean logic called Boolean Graph Logic (BGL). Construing formula trees as the cotrees of cographs, we may state semantic notions such as evaluation and entailment in purely graph-theoretic terms,…
In this note, by integrating ideas concerning terminating tableaux-based procedures in modal logics and finite frame property of intuitionistic modal logic IK, we provide new and simpler decidability proofs for FIK and LIK.
The methods used to establish PSPACE-bounds for modal logics can roughly be grouped into two classes: syntax driven methods establish that exhaustive proof search can be performed in polynomial space whereas semantic approaches directly…
A number of model-comparison games central to (finite) model theory, such as pebble and Ehrenfeucht-Fra\"{i}ss\'{e} games, can be captured as comonads on categories of relational structures. In particular, the coalgebras for these comonads…
In this paper we study frame definability in finitely-valued modal logics and establish two main results via suitable translations: (1) in finitely-valued modal logics one cannot define more classes of frames than are already definable in…