### Theses and Ph.D. Dissertation

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Ph.D. in Computer Science. Dissertation

**
"Semantics of Knowledge Based Systems with Multiple Forms of Negation"
**

In my Ph.D. thesis I introduced and investigated
formalisms that admit several forms of default negation
which interact with each other and with classical (or "explicit")
negation in the same knowledge based system.
Some theoretical aspects of this research include the investigation of the
expressive power of the new formalisms and
the characterization of their semantics.
Practical issues include implementing procedures to compute in these
formalisms, calculating the computational complexity of different reasoning
tasks under the proposed semantics and
modeling real life applications.
One example is the problem of merging several knowledge bases,
each of which uses a different rule for negation,
and finding answers to
queries in the combined knowledge base.

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M.S. in Computer Science. Thesis

** Formal Verification of Abstract Data Types and Code Synthesis.**

Designed and developed an environment for the definition and manipulation
of Abstract Data Types (ADTs), which provides a code synthesizer that
automatically generates code in LISP and/or C which structurally and
functionally implements an ADT. This code may be used in common
applications.
The environment includes also a theorem prover
oriented to perform formal verification of ADTs as well as proving
abstract properties of ADTs. It uses rewriting rules
to produce and deal with canonical forms of ADT expressions.

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B.S. in Mathematics. Undergraduate Thesis

** Categorical Logic.**

Showed that the category Dyn($\Sigma$) of automata and dynamorphisms
over an alphabet $\Sigma$, and of the category MooreMch($\Sigma$) of Moore
automata and Moore dynamorphisms over $\Sigma$ are presheaf topoi,
and investigated their exponentials and subobject classifiers.
Constructed free automata and free Moore automata over sets
by respectively using the left adjoints of the forgetful functors from
Dyn($\Sigma$) and MooreMch($\Sigma$) into the
category of sets (which assign to each automaton or Moore automaton its
set of states).
Proved that each regular language over $\Sigma$ corresponds to the
evaluation
of the characteristic morphism associated with the inclusion of the empty
subautomaton at the initial state of the accepting automaton.

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B.S. in Computer Science. Undergraduate Thesis

**Theorem Proving.**

Developed an implementation of the well-known theorem prover of R. Boyer
and
J.S. Moore characterized
by allowing the definition of inductive objects and recursive functions,
and
using induction on
well-founded orders as an essential part of theorem proving itself.