Related papers: On the Various Translations between Classical, Int…
We present a computational analysis of three language varieties: native, advanced non-native, and translation. Our goal is to investigate the similarities and differences between non-native language productions and translations, contrasting…
We investigate intuitionistic modal logics with locally interpreted $\square$ and $\lozenge$. The basic logic LIK is stronger than constructive modal logic WK and incomparable with intuitionistic modal logic IK. We propose an axiomatization…
This paper represents classical propositional proofs as *combinatorial proofs*, which are more abstract than proof nets: superposition (contraction/weakening) is modelled mathematically, as a lax form of fibration, rather than syntactically…
Although conventional logical systems based on logical calculi have been successfully used in mathematics and beyond, they have definite limitations that restrict their application in many cases. For instance, the principal condition for…
We introduce a non-associative and non-commutative version of propositional intuitionistic linear logic, called propositional non-associative non-commutative intuitionistic linear logic (NACILL for short). We prove that NACILL and any of…
The paper presents an extension of temporal epistemic logic with operators that quantify over strategies. The language also provides a natural way to represent what agents would know were they to be aware of the strategies being used by…
The formal construction of the second-order logic or predicate calculus essentially adds quantifiers to propositional logic. Why second-order logic cannot be reduced to that of the first order? How to demonstrate that certain predicates are…
In a previous work we introduced a non-associative non-commutative logic extended by multimodalities, called subexponentials, licensing local application of structural rules. Here, we further explore this system, considering a classical…
Computability logic is a formal theory of (interactive) computability in the same sense as classical logic is a formal theory of truth. This approach was initiated very recently in "Introduction to computability logic" (Annals of Pure and…
Possibilistic logic offers a qualitative framework for representing pieces of information associated with levels of uncertainty of priority. The fusion of multiple sources information is discussed in this setting. Different classes of…
A sound and complete embedding of conditional logics into classical higher-order logic is presented. This embedding enables the application of off-the-shelf higher-order automated theorem provers and model finders for reasoning within and…
Two interpretations about syllogistic statements are described in this paper. One is the so-called set-based interpretation, which assumes that quantified statements and syllogisms talk about quantity-relationships between sets. The other…
We study the notion of stratification, as used in subsystems of linear logic with low complexity bounds on the cut-elimination procedure (the so-called light logics), from an abstract point of view, introducing a logical system in which…
Focusing is a known technique for reducing the number of proofs while preserving derivability. Skolemisation is another technique designed to improve proof search, which reduces the number of back-tracking steps by representing dependencies…
Linear implication can represent state transitions, but real transition systems operate under temporal, stochastic or probabilistic constraints that are not directly representable in ordinary linear logic. We propose a general modal…
Building on our previous work on hybrid polyadic modal logic we identify modal logic equivalents for Matching Logic, a logic for program specification and verification. This provides a rigorous way to transfer results between the two…
Computability logic (CL) is a systematic formal theory of computational tasks and resources, which, in a sense, can be seen as a semantics-based alternative to (the syntactically introduced) linear logic. With its expressive and flexible…
A notion of interpretation between arbitrary logics is introduced, and the poset Log of all logics ordered under interpretability is studied. It is shown that in Log infima of arbitrarily large sets exist, but binary suprema in general do…
Interpolation is an important property of classical and many non classical logics that has been shown to have interesting applications in computer science and AI. Here we study the Interpolation Property for the propositional version of the…
Our manuscript studies linear temporal (with UNTIL and NEXT) logic based at a conception of intransitive time. non-transitive time. In particular, we demonstrate how the notion of knowledge might be represented in such a framework (here we…