Related papers: Tense distributive lattices: algebra, logic and to…
We present a novel asynchronous hyper linear time temporal logic named LPrL (Linear Time Predicate Logic) and establish its basic theory. LPrL is a natural first order extension of LTL (Linear time temporal logic), in which the predicates…
This paper introduces a dynamic logic extension of separation logic. The assertion language of separation logic is extended with modalities for the five types of the basic instructions of separation logic: simple assignment, look-up,…
Kolmogorov introduced an informal calculus of problems in an attempt to provide a classical semantics for intuitionistic logic. This was later formalised by Medvedev and Muchnik as what has come to be called the Medvedev and Muchnik…
This article initiates the semantic study of distribution-free normal modal logic systems, laying the semantic foundations and anticipating further research in the area. The article explores roughly the same area, though taking a different…
Besides the better-known Nelson logic (N3) and paraconsistent logic (N4), in 1959 David Nelson introduced, with motivations of realizability and constructibility, a logic called S. The logic S was originally presented by means of a calculus…
In this paper, we study logics of bounded distributive residuated lattices with modal operators considering $\Box$ and $\Diamond$ in a noncommutative setting. We introduce relational semantics for such substructural modal logics. We prove…
We establish a novel connection between two research areas in non-classical logics which have been developed independently of each other so far: on the one hand, input/output logic, introduced within a research program developing logical…
The preferential conditional logic PCL, introduced by Burgess, and its extensions are studied. First, a natural semantics based on neighbourhood models, which generalise Lewis' sphere models for counterfactual logics, is proposed. Soundness…
We develop a second-order extension of intuitionistic modal logic, allowing quantification over propositions, both syntactically and semantically. A key feature of second-order logic is its capacity to define positive connectives from the…
We present a multi-modal action logic with first-order modalities, which contain terms which can be unified with the terms inside the subsequent formulas and which can be quantified. This makes it possible to handle simultaneously time and…
Besides the better-known Nelson's Logic and Paraconsistent Nelson's Logic, in "Negation and separation of concepts in constructive systems" (1959), David Nelson introduced a logic called S with the aim of analyzing the constructive content…
The development of logic has largely been through the 'deductive' paradigm: conclusions are inferred from established premisses. However, the use of logic in the context of both human and machine reasoning is typically through the dual…
In this paper we introduce and study an alternative definition of tense operators on residuated lattices. We give a categorical equivalence for the class of tense residuated lattices, which is motivated by an old construction due to J.…
Logical formalisms for reasoning about relations between spatial regions play a fundamental role in geographical information systems, spatial and constraint databases, and spatial reasoning in AI. In analogy with Halpern and Shoham's modal…
Non-classical generalizations of classical modal logic have been developed in the contexts of constructive mathematics and natural language semantics. In this paper, we discuss a general approach to the semantics of non-classical modal…
A new totally algebraic formalism based on general, abstract ladder operators has been proposed. This approach heavily grounds in the superoperator formalism of Primas. However it is necessary to introduce many improvements in his…
We consider a simple modal logic whose non-modal part has conjunction and disjunction as connectives and whose modalities come in adjoint pairs, but are not in general closure operators. Despite absence of negation and implication, and of…
In the 1980s, category theorists introduced the Lawvere-Tierney $(\leq_{\mathrm{LT}})$ order in the Effective Topos, known to effectively embed the Turing degrees. Understanding its structure is a longstanding open problem in the area. In…
It is known that different categorial grammars have surface representation in a fragment of first order multiplicative linear logic (MLL1). We show that the fragment of interest is equivalent to the recently introduced extended tensor type…
Many complex scenarios require the coordination of agents possessing unique points of view and distinct semantic commitments. In response, standpoint logic (SL) was introduced in the context of knowledge integration, allowing one to reason…