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We determine all composition-closed equational classes of Boolean functions. These classes provide a natural generalization of clones and iterative algebras: they are closed under composition, permutation and identification…
In recent work, we introduced a new semantics for conditionals, covering a large class of what we call preconditionals. In this paper, we undertake an axiomatic study of preconditionals and subclasses of preconditionals. We then prove that…
We have previously introduced role logic as a notation for describing properties of relational structures in shape analysis, databases and knowledge bases. A natural fragment of role logic corresponds to two-variable logic with counting and…
We study the expressive power of the two-variable fragment of order-invariant first-order logic. This logic departs from first-order logic in two ways: first, formulas are only allowed to quantify over two variables. Second, formulas can…
We extend the logical categories framework to first order modal logic. In our modal categories, modal operators are applied directly to subobjects and interact with the background factorization system. We prove a Joyal-style representation…
We present a first-order logic equipped with an "asymmetric" directed notion of equality, which can be thought of as rewrites between terms, allowing for types to be interpreted as preorders. The logic is equipped with a precise syntactic…
We establish a novel connection between two research areas in non-classical logics which have been developed independently of each other so far: on the one hand, input/output logic, introduced within a research program developing logical…
Non-normal modal logics, interpreted on neighbourhood models which generalise the usual relational semantics, have found application in several areas, such as epistemic, deontic, and coalitional reasoning. We present here preliminary…
In this paper, we distinguish between two kinds of compositional data sets: elementary and aggregate. This fact will help us to decide the choice of the weights to use in log interaction analysis of aggregate compositional vectors. We show…
Charles Peirce develops a scheme for classifying different kinds of monadic, dyadic and triadic relations. His account of these different classes of relations figures prominently in the development of his algebraic and diagrammatic systems…
Most non-classical logics are subclassical, that is, every inference/theorem they validate is also valid classically. A notable exception is the three-valued propositional Logic of Ordinary Discourse (OL) proposed and extensively motivated…
Cumulative logics are studied in an abstract setting, i.e., without connectives, very much in the spirit of Makinson's early work. A powerful representation theorem characterizes those logics by choice functions that satisfy a weakening of…
In this paper we present methods of transition from one perspective on logic to others, and apply this in particular to obtain a coalgebraic presentation of logic. The central ingredient in this process is to view consequence relations as…
Classical AI planners provide solutions to planning problems in the form of long and opaque text outputs. To aid in the understanding transferability of planning solutions, it is necessary to have a rich and comprehensible representation…
This chapter presents a state-of-the-art survey of relationships, traditionally referred to as `bridges', between interpolation properties for propositional logics -- including superintuitionistic, modal, and substructural logics -- and…
We uncover a close relationship between combinatorial and syntactic proofs for first-order logic (without equality). Whereas syntactic proofs are formalized in a deductive proof system based on inference rules, a combinatorial proof is a…
First-order logic is typically presented as the study of deduction in a setting with elementary quantification. In this paper, we take another vantage point and conceptualize first-order logic as a linear space that encodes "plausibility".…
We study links between first-order formulas and arbitrary properties for families of theories, classes of structures and their isomorphism types. Possibilities for ranks and degrees for formulas and theories with respect to given properties…
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…
We present a family of minimal modal logics (namely, modal logics based on minimal propositional logic) corresponding each to a different classical modal logic. The minimal modal logics are defined based on their classical counterparts in…