Related papers: M\=im\=a\d{m}s\=a deontic logic: proof theory and …
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…
In this work we answer a long standing request for temporal embeddings of deontic STIT logics by introducing the multi-agent STIT logic TDS. The logic is based upon atemporal utilitarian STIT logic. Yet, the logic presented here will be…
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…
We extend the {\lambda}-calculus with constructs suitable for relational and functional-logic programming: non-deterministic choice, fresh variable introduction, and unification of expressions. In order to be able to unify…
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…
Modal logics have proved useful for many reasoning tasks in symbolic artificial intelligence (AI), such as belief revision, spatial reasoning, among others. On the other hand, mathematical morphology (MM) is a theory for non-linear analysis…
Cathoristic logic is a multi-modal logic where negation is replaced by a novel operator allowing the expression of incompatible sentences. We present the syntax and semantics of the logic including complete proof rules, and establish a…
We design a proof system for propositional classical logic that integrates two languages for Boolean functions: standard conjunction-disjunction-negation and binary decision trees. We give two reasons to do so. The first is…
The standard approach to logic in the literature in philosophy and mathematics, which has also been adopted in computer science, is to define a language (the syntax), an appropriate class of models together with an interpretation of…
Graded modal logics generalise standard modal logics via families of modalities indexed by an algebraic structure whose operations mediate between the different modalities. The graded "of-course" modality $!_r$ captures how many times a…
This paper develops a logic based on causal inferences to formally capture the concept of instrumental obligation. We establish a causal deontic model that extends causal models with priority structures, allowing us to represent both the…
Justification logics are an explication of modal logic; boxes are replaced with proof terms formally through realisation theorems. This can be achieved syntactically using a cut-free proof system e.g. using sequent, hypersequent or nested…
Deep inference is a proof theoretic methodology that generalizes the standard notion of inference of the sequent calculus, whereby inference rules become applicable at any depth inside logical expressions. Deep inference provides more…
In this paper, we use a new method to prove cut-elimination of weak intuitionistic tense logic. This method focuses on splitting the contraction rule and cut rules. Further general theories and applications of this method shall be developed…
We present a embedding of Lewis Deontic logics in PUC-Logic. We achieve this by representing the vary basic $\boldsymbol{CO}$ logic and showing its relative completeness.
We present a simpler way than usual to deduce the completeness theorem for the second-oder classical logic from the first-order one. We also extend our method to the case of second-order intuitionistic logic.
In this survey, we present in a unified way the categorical and syntactical settings of coherent differentiation introduced recently, which shows that the basic ideas of differential linear logic and of the differential lambda-calculus are…
We give a linear nested sequent calculus for the basic normal tense logic Kt. We show that the calculus enables backwards proof-search, counter-model construction and syntactic cut-elimination. Linear nested sequents thus provide the…
The basic notions of logic-predicate logic, Peano arithmetic, incompleteness theorems, etc.-have for long been an advanced topic. In the last decades, they became more widely taught, inphilosophy, mathematics, and computer science…
In the last decade, formal logics have been used to model a wide range of ethical theories and principles with the goal of using these models within autonomous systems. Logics for modeling ethical theories, and their automated reasoners,…