The Soft Logic of Thomas Harriot
The strength of Turing determinacy within second order arithmetic
We investigate the reverse mathematical strength of Turing determinacy up to Σ₅⁰, which is itself not provable in second order arithmetic.
The study on semicopula based implications
Recently, Baczyński et al. (2017) proposed a new family of implication operators called semicopula based implications, which combines a given a priori fuzzy implication and a semicopula. In this paper, firstly, the relationship between the basic properties of the priori fuzzy implication and the semicopula based implication are analyzed. Secondly, the conditions such that the semicopula based implication is a fuzzy implication are studied, the study is carried out mainly in the case that the semicopula...
The theory of abelian p-groups with the quantifier I is decidable
The theory of Archimedean real closed fields in logics with Ramsey quantifiers
The theory of boolean algebras with a distinguished subalgebra is undecidable
The theory of differentially closed fields in logics with cardinal quantifiers.
The Theory of Successor with an Extra Predicate.
The Undecidability of Pseudo Real Closed Fields.
Theorem Provers for Substructural Logics
Théorème de Church-Rosser et structuration des langues naturelles
Theorem-proving systems [Book]
Théorie des modèles pour des anneaux de fonctions entières et des corps de fonctions méromorphes
Theorien abelscher Gruppen mit einem einstelligen Prädikat
Theories of orders on the set of words
It is shown that small fragments of the first-order theory of the subword order, the (partial) lexicographic path ordering on words, the homomorphism preorder, and the infix order are undecidable. This is in contrast to the decidability of the monadic second-order theory of the prefix order [M.O. Rabin, Trans. Amer. Math. Soc., 1969] and of the theory of the total lexicographic path ordering [P. Narendran and M. Rusinowitch, Lect. Notes Artificial Intelligence, 2000] and, in case of the subword...
Theories of orders on the set of words
It is shown that small fragments of the first-order theory of the subword order, the (partial) lexicographic path ordering on words, the homomorphism preorder, and the infix order are undecidable. This is in contrast to the decidability of the monadic second-order theory of the prefix order [M.O. Rabin, Trans. Amer. Math. Soc., 1969] and of the theory of the total lexicographic path ordering [P. Narendran and M. Rusinowitch, Lect. Notes Artificial Intelligence, 2000] and, in case of the ...
Theory of types and data description
Three notes on the complexity of model checking fixpoint logic with chop
This paper analyses the complexity of model checking fixpoint logic with Chop – an extension of the modal μ-calculus with a sequential composition operator. It uses two known game-based characterisations to derive the following results: the combined model checking complexity as well as the data complexity of FLC are EXPTIME-complete. This is already the case for its alternation-free fragment. The expression complexity of FLC is trivially P-hard and limited from above by the complexity of solving...
Three semantical interpretations of a statistical theoremhood testing procedure
Three-quantifier sentences
We give a complete proof that all 3-quantifier sentences in the primitive notation of set theory (∈, =), are decided in ZFC, and in fact in a weak fragment of ZF without the power set axiom. We obtain information concerning witnesses of 2-quantifier formulas with one free variable. There is a 5-quantifier sentence that is not decided in ZFC (see [2]).