23 research outputs found
The intuitionistic fragment of computability logic at the propositional level
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 between a machine and its environment. Intuitionistic
implication is understood as algorithmic reduction in the weakest possible --
and hence most natural -- sense, disjunction and conjunction as
deterministic-choice combinations of problems (disjunction = machine's choice,
conjunction = environment's choice), and "absurd" as a computational problem of
universal strength. See http://www.cis.upenn.edu/~giorgi/cl.html for a
comprehensive online source on computability logic
A new face of the branching recurrence of computability logic
This letter introduces a new, substantially simplified version of the
branching recurrence operation of computability logic (see
http://www.cis.upenn.edu/~giorgi/cl.html), and proves its equivalence to the
old, "canonical" version
Separating the basic logics of the basic recurrences
This paper shows that, even at the most basic level, the parallel, countable
branching and uncountable branching recurrences of Computability Logic (see
http://www.cis.upenn.edu/~giorgi/cl.html) validate different principles
Introduction to clarithmetic II
The earlier paper "Introduction to clarithmetic I" constructed an axiomatic
system of arithmetic based on computability logic (see
http://www.cis.upenn.edu/~giorgi/cl.html), and proved its soundness and
extensional completeness with respect to polynomial time computability. The
present paper elaborates three additional sound and complete systems in the
same style and sense: one for polynomial space computability, one for
elementary recursive time (and/or space) computability, and one for primitive
recursive time (and/or space) computability
A logical basis for constructive systems
The work is devoted to Computability Logic (CoL) -- the
philosophical/mathematical platform and long-term project for redeveloping
classical logic after replacing truth} by computability in its underlying
semantics (see http://www.cis.upenn.edu/~giorgi/cl.html). This article
elaborates some basic complexity theory for the CoL framework. Then it proves
soundness and completeness for the deductive system CL12 with respect to the
semantics of CoL, including the version of the latter based on polynomial time
computability instead of computability-in-principle. CL12 is a sequent calculus
system, where the meaning of a sequent intuitively can be characterized as "the
succedent is algorithmically reducible to the antecedent", and where formulas
are built from predicate letters, function letters, variables, constants,
identity, negation, parallel and choice connectives, and blind and choice
quantifiers. A case is made that CL12 is an adequate logical basis for
constructive applied theories, including complexity-oriented ones