Related papers: On inclusions between quantified provability logic…
In the same sense as classical logic is a formal theory of truth, the recently initiated approach called computability logic is a formal theory of computability. It understands (interactive) computational problems as games played by a…
We study the expressive power of fragments of inclusion and independence logic defined either by restricting the number of universal quantifiers or the arity of inclusion and independence atoms in formulas. Assuming the so-called lax…
The likelihood function represents statistical evidence in the context of data and a probability model. Considerable theory has demonstrated that evidence strength for different parameter values can be interpreted from the ratio of…
In this paper, we advocate the use of stratified logical theories for representing probabilistic models. We argue that such encodings can be more interpretable than those obtained in existing frameworks such as Markov logic networks. Among…
We combine the concepts of modal logics and many-valued logics in a general and comprehensive way. Namely, given any finite linearly ordered set of truth values and any set of propositional connectives defined by truth tables, we define the…
This paper presents a soundness and completeness proof for propositional intuitionistic calculus with respect to the semantics of computability logic. The latter interprets formulas as interactive computational problems, formalized as games…
We introduce ologisms. They generate from ologs by extending their logical expressivity, from the possibility of considering constraints of equational nature only to the possibility of considering constraints of syllogistic nature, in…
We extend classical Propositional Logic (PL) by adding a new primitive binary connective $\varphi|\psi$, intended to represent the "superposition" of sentences $\varphi$ and $\psi$, an operation motivated by the corresponding notion of…
We introduce some new logics of imperfect information by adding atomic formulas corresponding to inclusion and exclusion dependencies to the language of first order logic. The properties of these logics and their relationships with other…
We present a linearity theorem for a proof language of intuitionistic multiplicative additive linear logic, incorporating addition and scalar multiplication. The proofs in this language are linear in the algebraic sense. This work is part…
Relational verification of quantum programs has many potential applications in quantum and post-quantum security and other domains. We propose a relational program logic for quantum programs. The interpretation of our logic is based on a…
Despite extensive theoretical research on proportionality in approval-based multiwinner voting, its impact on which committees and candidates can be selected in practice remains poorly understood. We address this gap by (i) analyzing the…
We consider the immediate consequence of an arguable addition to the standard Deduction Theorems of first order theories.
In this survey we review dynamic epistemic logics with modalities for quantification over information change. Of such logics we present complete axiomatizations, focussing on axioms involving the interaction between knowledge and such…
We obtain a set of necessary and sufficient conditions for $| \bar{N}, p_{n} |_{k} $ to imply $|\bar{N}, q_{n} |_{s}$ for $1 < k \leq s < \infty$. Using this result we establish several inclusion theorems as well as conditions for the…
In probabilistic logic entailments, even moderate size problems can yield linear constraint systems with so many variables that exact methods are impractical. This difficulty can be remedied in many cases of interest by introducing a three…
This paper concerns an expansion of first-order Belnap-Dunn logic whose connectives and quantifiers all have a counterpart in classical logic. The language and logical consequence relation of this paradefinite logic are defined, a sequent…
We consider several examples of probabilistic existence proofs using compressibility arguments, including some results that involve Lov\'asz local lemma.
Probability theory as extended logic is completed such that essentially any probability may be determined. This is done by considering propositional logic (as opposed to predicate logic) as syntactically suffcient and imposing a symmetry…
One of the nice properties of the first-order logic is the compactness of satisfiability. It state that a finitely satisfiable theory is satisfiable. However, different degrees of satisfiability in many-valued logics, poses various kind of…