Related papers: A polynomial time complete disjunction property in…
Reasoning under uncertainty is a fundamental challenge in Artificial Intelligence. As with most of these challenges, there is a harsh dilemma between the expressive power of the language used, and the tractability of the computational…
We prove that there is a factor of the Muchnik lattice that captures intuitionistic propositional logic. This complements a now classic result of Skvortsova for the Medvedev lattice.
Recently, B\'{e}nyi and the second author introduced two combinatorial interpretations for symmetrized poly-Bernoulli polynomials. In the present study, we construct bijections between these combinatorial objects. We also define various…
Interval Temporal Logic (ITL) is an established temporal formalism for reasoning about time periods. For over 25 years, it has been applied in a number of ways and several ITL variants, axiom systems and tools have been investigated. We…
The languages of logics based on team semantics typically only allow atomic negation or restricted negation. In this paper, we explore propositional team-based logics with full (intuitionistic) negation. We demonstrate that including full…
This paper continues an established line of research about the relations between argumentation theory, particularly assumption-based argumentation, and different kinds of logic programs. In particular, we extend known result of Caminada,…
The recent work by Marcus, Spielman and Srivastava proves the existence of bipartite Ramanujan (multi)graphs of all degrees and all sizes. However, that paper did not provide a polynomial time algorithm to actually compute such graphs.…
It is well known that the resolution method (for propositional logic) is complete. However, completeness proofs found in the literature use an argument by contradiction showing that if a set of clauses is unsatisfiable, then it must have a…
We address the problem of propositional logic-based abduction, i.e., the problem of searching for a best explanation for a given propositional observation according to a given propositional knowledge base. We give a general algorithm, based…
We extend Choiceless Polynomial Time (CPT), the currently only remaining promising candidate in the quest for a logic capturing PTime, so that this extended logic has the following property: for every class of structures for which…
We consider intuitionistic variants of linear temporal logic with `next', `until' and `release' based on expanding posets: partial orders equipped with an order-preserving transition function. This class of structures gives rise to a logic…
The language of linear temporal logic can be interpreted over the class of dynamic topological systems, giving rise to the intuitionistic temporal logic ${{\sf ITL}^{\sf c}}_{\Diamond,\forall}$, recently shown to be decidable by…
This paper provides a new version of the condition of Di Nunno et al. (2003), Ankirchner and Imkeller (2005) and Biagini and \{O}ksendal (2005) ensuring the semimartingale property for a large class of continuous stochastic processes.…
Propositional formulas that are equivalent in intuitionistic logic, or in its extension known as the logic of here-and-there, have the same stable models. We extend this theorem to propositional formulas with infinitely long conjunctions…
We first present a Priestley-style dualitiy for the classes of algebras that are the algebraic counterpart of some congruential, finitary and filter-distributive logic with theorems. Then we analyze which properties of the dual spaces…
In order to prove that the P of problems is different to the NP class, we consider the satisfability problem of propositional calculus formulae, which is an NP-complete problem. It is shown that, for every search algorithm A, there is a set…
We propose a new type system for lambda-calculus ensuring that well-typed programs can be executed in polynomial time: Dual light affine logic (DLAL). DLAL has a simple type language with a linear and an intuitionistic type arrow, and one…
On the one hand, classical logic is an extremely successful theory, even if not being perfect. On the other hand, intuitionistic logic is, without a doubt, one of the most important non-classical logics. But, how can proponents of one logic…
We provide a numerical refutation of the developments of Fiorini et al. (2015)* for models with disjoint sets of descriptive variables. We also provide an insight into the meaning of the existence of a one-to-one linear map between…
For a given intuitionistic propositional formula A and a propositional variable x occurring in it, define the infinite sequence of formulae { A \_i | i$\ge$1} by letting A\_1 be A and A\_{i+1} be A(A\_i/x). Ruitenburg's Theorem [8] says…