Related papers: A complete system of deduction for Sigma formulas
In this paper we characterize the congruence associated to the direct sum of all irreducible representations of a finite semigroup over an arbitrary field, generalizing results of Rhodes for the field of complex numbers. Applications are…
We consider an extension of first-order logic with a recursion operator that corresponds to allowing formulas to refer to themselves. We investigate the obtained language under two different systems of semantics, thereby obtaining two…
This paper introduces Sigma, a domain-specific computational representation for collaboration in large-scale for the field of economics. A computational representation is not a programming language or a software platform. A computational…
Causal reasoning in relational domains is fundamental to studying real-world social phenomena in which individual units can influence each other's traits and behavior. Dynamics between interconnected units can be represented as an…
In this paper we will see deductive systems for classical propositional and predicate logic in the calculus of structures. Like sequent systems, they have a cut rule which is admissible. In addition, they enjoy a top-down symmetry and some…
The development of logic has largely been through the 'deductive' paradigm: conclusions are inferred from established premisses. However, the use of logic in the context of both human and machine reasoning is typically through the dual…
In this paper we introduce sigma limits (which we write $\sigma$-limits), a concept that interpolates between lax and pseudolimits: for a fixed family $\Sigma$ of arrows of a 2-category $\mathcal{A}$, a $\sigma$-cone for a $2$-functor…
Informally speaking, the categoricity of an axiom system means that its non-logical symbols have only one possible interpretation that renders the axioms true. Although non-categoricity has become ubiquitous in the second half of the 20th…
Complexity and decidability of logics is a major research area involving a huge range of different logical systems. This calls for a unified and systematic approach for the field. We introduce a research program based on an algebraic…
The implication relationship between subsystems in Reverse Mathematics has an underlying logic, which can be used to deduce certain new Reverse Mathematics results from existing ones in a routine way. We use techniques of modal logic to…
A program schema defines a class of programs, all of which have identical statement structure, but whose functions and predicates may differ. A schema thus defines an entire class of programs according to how its symbols are interpreted. A…
This paper proves normalisation theorems for intuitionist and classical negative free logic, without and with the $\invertediota$ operator for definite descriptions. Rules specific to free logic give rise to new kinds of maximal formulas…
We present a comprehensive programme analysing the decomposition of proof systems for non-classical logics into proof systems for other logics, especially classical logic, using an algebra of constraints. That is, one recovers a proof…
We extend two well-known results on primitive ideals in enveloping algebras of semisimple Lie algebras, the `Irreducibility theorem' and `Duflo theorem', to much wider classes of algebras. Our general version of Irreducibility theorem says…
The general setting of this work is the constraint-based synthesis of termination arguments. We consider a restricted class of programs called lasso programs. The termination argument for a lasso program is a pair of a ranking function and…
We show that no total functional can uniformly transform $\Pi_1$ primality into explicit $\Sigma_1$ witnesses without violating normalization in $\mathsf{HA}$. The argument proceeds through three complementary translations: a geometric…
We study the relative complexity of equivalence relations and preorders from computability theory and complexity theory. Given binary relations $R, S$, a componentwise reducibility is defined by $ R\le S \iff \ex f \, \forall x, y \, [xRy…
Simpson and the second author asked whether there exists a characterization of the natural numbers by a second-order sentence which is provably categorical in the theory RCA$^*_0$. We answer in the negative, showing that for any…
Modal formulae express monadic second-order properties on Kripke frames, but in many important cases these have first-order equivalents. Computing such equivalents is important for both logical and computational reasons. On the other hand,…
Our concern is the completeness problem for spi-logics, that is, sets of implications between strictly positive formulas built from propositional variables, conjunction and modal diamond operators. Originated in logic, algebra and computer…