Related papers: Pretabular Tense Logics over S4t
Logical relations constitute a key method for reasoning about contextual equivalence of programs in higher-order languages. They are usually developed on a per-case basis, with a new theory required for each variation of the language or of…
Nonmonotonic logics are usually characterized by the presence of some notion of 'conditional' that fails monotonicity. Research on nonmonotonic logics is therefore largely concerned with the defeasibility of argument forms and the…
Lindstr\"om's Theorem characterizes first order logic as the maximal logic satisfying the Compactness Theorem and the Downward L\"owenheim-Skolem Theorem. If we do not assume that logics are closed under negation, there is an obvious…
Regular tree grammars and regular path expressions constitute core constructs widely used in programming languages and type systems. Nevertheless, there has been little research so far on reasoning frameworks for path expressions where node…
In this paper we present the first-order logic QLETF+, a quantified version of the logic LETF+, introduced in Coniglio and Rodrigues (Studia Logica 112:561-606, 2024). QLETF+ exhibits several properties that are not always enjoyed by logics…
Strategy Logic (SL) is a logical formalism for strategic reasoning in multi-agent systems. Its main feature is that it has variables for strategies that are associated to specific agents with a binding operator. We introduce Graded Strategy…
For each natural number $n$ we study the modal logic determined by the class of transitive Kripke frames in which there are no cycles of length greater than $n$ and no strictly ascending chains. The case $n=0$ is the G\"odel-L\"ob…
G3-style sequent calculi for the logics in the cube of non-normal modal logics and for their deontic extensions are studied. For each calculus we prove that weakening and contraction are height-preserving admissible, and we give a syntactic…
Prior research in computational argumentation has mainly focused on scoring the quality of arguments, with less attention on explicating logical errors. In this work, we introduce four sets of explainable templates for common informal…
A logic-enriched type theory (LTT) is a type theory extended with a primitive mechanism for forming and proving propositions. We construct two LTTs, named LTTO and LTTO*, which we claim correspond closely to the classical predicative…
We extend the simply-typed guarded $\lambda$-calculus with discrete probabilities and endow it with a program logic for reasoning about relational properties of guarded probabilistic computations. This provides a framework for programming…
We adjust the notion of finitary filter pair, which was coined for creating and analyzing finitary logics, in such a way that we can treat logics of cardinality $\kappa$, where $\kappa$ is a regular cardinal. The corresponding new notion is…
This paper introduces an abstract notion of fragments of monadic second-order logic. This concept is based on purely syntactic closure properties. We show that over finite words, every logical fragment defines a lattice of languages with…
A class of interval-based temporal languages for uniformly representing and reasoning about actions and plans is presented. Actions are represented by describing what is true while the action itself is occurring, and plans are constructed…
We provide a version of first-order hybrid tense logic with predicate abstracts and definite descriptions as the only non-rigid terms. It is formalised by means of a tableau calculus working on sat-formulas. A particular theory of DD…
A proof procedure, in the spirit of the sequent calculus, is proposed to check the validity of entailments between Separation Logic formulas combining inductively defined predicates denoted structures of bounded tree width and theory…
While reasoning in a logic extending a complete Boolean basis is coNP-hard, restricting to conjunctive fragments of modal languages sometimes allows for tractable reasoning even in the presence of greatest fixpoints. One such example is the…
We establish the decidability of the $\Sigma_2$ theory of both the arithmetic and hyperarithmetic degrees in the language of uppersemilattices i.e. the language with $\leq, 0$ and $\sqcup$. This is achieved by using Kumabe-Slaman forcing -…
This paper falls within the general program of investigating the proof theoretic strength (in terms of reverse mathematics) of combinatorial principals which follow from versions of Ramsey's theorem. We examine two statements in graph…
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…