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A bi-Heyting algebra validates the Go ̈del-Dummett axiom (p → q) ∨ (q → p) iff the poset of its prime filters is a disjoint union of co-trees (i.e., order duals of trees). Bi-Heyting algebras of this form are called bi-Go ̈del algebras and form a variety that algebraizes the extension bi-LC of bi...
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We present a number of puzzles arising for the interpretation of mod-
ified numerals. Following Büring and others we assume that the main
difference between comparative and superlative modifiers is that only the latter convey disjunctive meanings. We further argue that the inference patterns tr...
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In this paper we present a topological epistemic logic, with modalities for knowledge (modeled as the universal modality), knowability (represented by the topological interior operator), and unknowability of the actual world. The last notion has a non-self-referential reading (modeled by Cantor d...
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This paper presents a new uniform method for studying modal companions of superintuitionistic deductive systems and related notions, based on the machinery of stable canonical rules. Using our method, we obtain an al- ternative proof of the Blok-Esakia theorem both for logics and for rule systems...
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We present a novel treatment of set theory in a four-valued paracomplete and paraconsistent logic, i.e., a logic in which propositions can be neither true nor false, and can be both true and false. By prioritising a system with an ontology of non-classical sets that is easy to understand and appl...
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We put forward a formal model of participatory budgeting where projects can incur costs with respect to several different resources, such as money, energy, or emission allowances. We generalise several well-known mechanisms from the usual single-resource setting to this multi-resource setting and...
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Finite Turing computation has a fundamental symmetry between inputs, outputs, programs, time, and storage space.
Standard models of transfinite computational break this symmetry; we consider ways to recover it and study the resulting model of computation.
This model exhibits the same symmetry
...
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We present sound and complete sequent calculi for the modal mu-calculus with converse modalities, aka two-way modal mu-calculus. Notably, we introduce a cyclic proof system wherein proofs can be represented as finite trees with back-edges, i.e., finite graphs. The sequent calculi incorporate ordi...
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A classic result in modal logic, known as the Blok Dichotomy Theorem, states that the degree of incompleteness of a normal extension of the basic modal logic K is 1 or the continuum. It is a long-standing open problem whether Blok Dichotomy holds for normal extensions of other prominent modal log...
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We investigate a recent semantics for intermediate (and modal) logics in terms of polyhedra. The main result is a finite axiomatisation of the intermediate logic of the class of all polytopes — i.e., compact convex polyhedra — denoted PL. This logic is defined in terms of the Jankov-Fine formulas...
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In this paper we present a general theory of Π2-rules for systems of intuitionistic and modal logic. We introduce the notions of Π2-rule system and of an Inductive Class, and provide model-theoretic and algebraic completeness theorems, which serve as our basic tools. As an illustration of the gen...