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Despite recent advances in automating theorem proving in full first-order theories, inductive reasoning still poses a serious challenge to state-of-the-art theorem provers. The reason for that is that in first-order logic induction requires…

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…

We design various logics for proving hyper properties of iterative programs by application of abstract interpretation principles. In part I, we design a generic, structural, fixpoint abstract interpreter parameterized by an algebraic…

We present Hypersequent Classical Processes (HCP), a revised interpretation of the "Proofs as Processes" correspondence between linear logic and the {\pi}-calculus initially proposed by Abramsky [1994], and later developed by Bellin and…

This paper has two goals. The first goal is to show how an extension of second-order logic is a natural framework to formalize portions of Aristotle's \emph{Topics} and to bring to the foreground the logical, linguistic and philosophical…

It is well known that many-sorted logic can be reduced to unsorted first-order logic by adding predicates for each sort, relativizing quantifiers to these predicates, and adding appropriate axioms governing their behavior. Existing…

This paper examines the complexity of hybrid logics over transitive frames, transitive trees, and linear frames. We show that satisfiability over transitive frames for the hybrid language extended with the downarrow operator is…

Graded modal logic is the formal language obtained from ordinary (propositional) modal logic by endowing its modal operators with cardinality constraints. Under the familiar possible-worlds semantics, these augmented modal operators receive…

Regarding the famous Sea Battle Argument, which Aristotle presents in De Interpretatione 9, there has never been a general agreement not only about its correctness but also, and mainly, about what the argument really is. According to the…

We give sound and complete Hilbert-style axiomatizations for propositional dependence logic (PD), modal dependence logic (MDL), and extended modal dependence logic (EMDL) by extending existing axiomatizations for propositional logic and…

We propose a fragment of many-sorted second order logic called EQSMT and show that checking satisfiability of sentences in this fragment is decidable. EQSMT formulae have an $\exists^*\forall^*$ quantifier prefix (over variables, functions…

There is a problem with the foundations of classical mathematics, and potentially even with the foundations of computer science, that mathematicians have by-and-large ignored. This essay is a call for practicing mathematicians who have been…

We provide a complete axiomatization of modal inclusion logic - team-based modal logic extended with inclusion atoms. We review and refine an expressive completeness and normal form theorem for the logic, define a natural deduction proof…

We show that a partial-correctness assertion about an iterative program is provable in Hoare Logic iffit is provable in standard second-order logic with comprehension restricted to first-order predicates. This equivalence was claimed twice…

We introduce the calculus of Classical Transitions (CT), which extends the research line on the relationship between linear logic and processes to labelled transitions. The key twist from previous work is registering parallelism in typing…

It is generally accepted that quantum mechanics entails a revision of the classical propositional calculus as a consequence of its physical content. However, the universal claim according to which a new quantum logic is indispensable in…

We study various formulations of the completeness of first-order logic phrased in constructive type theory and mechanised in the Coq proof assistant. Specifically, we examine the completeness of variants of classical and intuitionistic…

The modal systems S1--S3 were introduced by C. I. Lewis as logics for strict implication. While there are Kripke semantics for S2 and S3, there is no known natural semantics for S1. We extend S1 by a Substitution Principle SP which…

We introduce a family of modal expansions of {\L}ukasiewicz logic that are designed to accommodate modal translations of generalized basic logic (as formulated with exchange, weakening, and falsum). We further exhibit algebraic semantics…

Scientific claim verification against tables typically requires predicting whether a claim is supported or refuted given a table. However, we argue that predicting the final label alone is insufficient: it reveals little about the model's…