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We construct witnesses that can be used to derive strategies in fixpoint games and provide proof that the least fixpoint of a function is either above or not below some given bound. We rely on a lattice-theoretical approach, including a…
In this paper a conditional logic is defined and studied. This conditional logic, DmBL, is constructed as a deterministic counterpart to the Bayesian conditional. The logic is unrestricted, so that any logical operations are allowed. A…
We propose a generalization of first-order logic originating in a neglected work by C.C. Chang: a natural and generic correspondence language for any types of structures which can be recast as Set-coalgebras. We discuss axiomatization and…
The use of meta-rules in logic, i.e., rules whose content includes other rules, has recently gained attention in the setting of non-monotonic reasoning: a first logical formalisation and efficient algorithms to compute the (meta)-extensions…
This paper aims to provide an analysis of what it means when we say that a pair of theories, very generously construed, are equivalent in the sense that they are interdefinable. With regard to theories articulated in first order logic, we…
The paper proposes a derivation system for a logic of presuppositions as introduced by P. F. Strawson. It is based on truth-relevant logic described by M. Richard Diaz in 1981. In another paper I outlined a derivation system for t-relevant…
We study probabilistic team semantics which is a semantical framework allowing the study of logical and probabilistic dependencies simultaneously. We examine and classify the expressive power of logical formalisms arising by different…
In this paper, we introduce a logic based on team semantics, called FOT, whose expressive power is elementary, i.e., coincides with first-order logic both on the level of sentences and (possibly open) formulas, and we also show that a…
The rule "defeated(X) $\leftarrow$ attacks(Y,X), $\neg$ defeated(Y)" states that an argument is defeated if it is attacked by an argument that is not defeated. The rule "win(X) $\leftarrow$ move(X,Y), $\neg$ win(Y)" states that in a game a…
Ehrenfeucht-Fraisse games are very useful in studying separation and equivalence results in logic. The standard finite Ehrenfeucht-Fraisse game characterizes equivalence in first order logic. The standard Ehrenfeucht-Fraisse game in…
We propose a new version of formula size game for modal logic. The game characterizes the equivalence of pointed Kripke-models up to formulas of given numbers of modal operators and binary connectives. Our game is similar to the well-known…
We consider the termination/non-termination property of a class of loops. Such loops are commonly used abstractions of real program pieces. Second-order logic is a convenient language to express non-termination. Of course, such property is…
Higher-order logic HOL offers a very simple syntax and semantics for representing and reasoning about typed data structures. But its type system lacks advanced features where types may depend on terms. Dependent type theory offers such a…
There is knowledge. There is belief. And there is tacit agreement.' 'We may talk about objects. We may talk about attributes of the objects. Or we may talk both about objects and their attributes.' This work inspects tacit agreements on…
We propose a framework for modeling uncertainty where both belief and doubt can be given independent, first-class status. We adopt probability theory as the mathematical formalism for manipulating uncertainty. An agent can express the…
We introduce a proper display calculus for (non-distributive) Lattice Logic which is sound, complete, conservative, and enjoys cut-elimination and sub-formula property. Properness (i.e. closure under uniform substitution of all parametric…
We investigate a version of linear temporal logic whose propositional fragment is G\"odel-Dummett logic (which is well known both as a superintuitionistic logic and a t-norm fuzzy logic). We define the logic using two natural semantics:…
In Apt and Bezem [AB99] (see cs.LO/9811017) we provided a computational interpretation of first-order formulas over arbitrary interpretations. Here we complement this work by introducing a denotational semantics for first-order logic.…
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…
Coalition Logic is a central logic in logical research on strategic reasoning. In a recent paper, Li and Ju argued that generally, models of Coalition Logic, concurrent game models, have three too strong assumptions: seriality, independence…