# Questions tagged [lo.logic]

Computational and mathematical logic.

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0answers
149 views

### Counting solutions to extended MSO formulas, and sampling — do these appear in the literature?

I am trying to determine if the literature contains various extensions of Courcelle's theorem. Since I haven't been able to find these in the literature, I guess that these are folklore results, or ...
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78 views

### Forward chaining algorithms

I am interested in learning about the current state of the art regarding forward chaining production systems. I understand that things haven't changed much (regarding the basic algorithms) since 1995'...
0answers
202 views

### Reverse Skolemization?

I'm wondering if there are any references on "reverse skolemization", that is, converting a formula with functions into one purely consisting of quantifiers by eliminating function applications. I'm ...
1answer
85 views

### How to build comparison operator (comparator) in an arithmetic circuit

I am trying to convert a basic program into an arithmetic circuit. I am stuck on the step of converting the greater than operator into an arithmetic circuit. To be specific, I do not know how to ...
0answers
69 views

### What is sequence unification?

And why is it interesting? Please provide some examples. This text is here to circumvent the anti-spam filter which thinks my question is bad.
2answers
201 views

### How do continuations represent negations (under the Curry–Howard correspondence)?

Under the Curry–Howard correspondence, types can be thought of as propositions, and values inhabiting a type can be thought of as proofs that the corresponding proposition is true. (E.g., the ...
0answers
43 views

### Extending the sequential calculus (logic over words) to allow a hierarchy of languages like the arithmetical hierarchy

Let $\Sigma$ be some finite alphabet. Then consider the logical language $\mathcal L = \{ R_a : a \in \Sigma \} \cup \{ <,= \}$ and first order formulas. For a given first order formula $\varphi$ a ...
1answer
127 views

### Reductions in Descriptive Complexity

Reducing one problem to another are well known in various settings, such as many-one, randomized, truth-table, logspace or a whole slew of other reductions. Descriptive complexity can alternately ...
0answers
94 views

### Notion of “quotient” or “inverse” for recognizable tree languages?

Related to my previous question but this time I have a better idea of what I'm actually asking. I'm looking at the following operation on recognizable tree languages (i.e. regular tree grammars, ...
2answers
616 views

### What logic correponds via Curry-Howard to a Monad?

According to Moggi's 1991 paper "Notions of computation and monads" one can represent monadic equational logic with the well known monad $(T, \eta, \mu)$ with T an functor and the two natural ...
2answers
151 views

### Compactness of domino tilings

I've read in Lemma 2 of the paper 1 that if every square region of the plane admits a tiling, then the whole plain admits a tiling, but the proof is omitted. This sounds like a compactness property, ...
1answer
112 views

### Dependent C-style types with subtyping rule

I'm looking for previous work regarding an extension of a C-style type system in which types may have constraints and have a defined subtyping rule. In particular, I'm interested in defining algebra-...
1answer
252 views

### What is the reference for the proof Gödel's first incompleteness theorem based on the undecidability of the halting problem?

A weaker form of Gödel's First Incompleteness Theorem, direct proofs of which in Gödel's manner are lengthy, involved and at some place rather counter-intuitive, has a simple and intuitive proof based ...
1answer
174 views

### P and Descriptive Complexity

In the Complexity Zoo, it says  that, in descriptive complexity, $P$ can be defined by three different kind of formulae, $FO(LFP)$ which is also $FO(n^{O(1)})$, and also as $SO(HORN)$. However, ...
2answers
231 views

1answer
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### What's the difference between proving weak normalization and implementing evaluator?

Implementing an normalization (cut elimination) procedure for a type system A in a language with a total type system B, automatically proves cut elimination for type system A since the implementation ...
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193 views

### Is it possible to type Ackermann function with (stratified variant of) System F?

I was surprised to find no open-source implementation of Ackermann function in pure System F as an illustrative example. I finally managed to implement it myself in Haskell using Church encoding: <...
1answer
101 views

### Is there a formalization of normalization of impredicative system F?

In particular Agda seems not strong enough to prove that. Is the predicative Calculus of Inductive Constructions universes (Coq without Prop) sufficient? How about with the impredicative Prop?
1answer
52 views

### Is there a standard format for Dependent QBF?

I know there is a standard input format DIMACS for a formula is in conjunctive normal form (CNF) and QDIMACS for quantified Boolean formulas. Is there a similar standard format for the Dependent-QBF (...
1answer
119 views

### Does this variant of Multiplicative Linear Logic with mix rule enjoy cut elimination?

In Multiplicative Linear Logic (MLL), addition of the mix rule eliminates 'connectedness' from Danos-Regnier criterion. I'm investigating how the criterion changes if we do not distinguish between ...
1answer
47 views

### Algorithm for finding smallest set and instanciation for a given constraint system

I have a system of constraints described by a set of clauses of the form $x_1 \neq x_2 \lor \dots \lor x_{i-1} \neq x_i$, for instance: ...
0answers
57 views

### To what extent supervised learning ERM learn first-order knowledge

Suppose I have a collection of (hidden) first-order rules: $$\mathcal{R}: \{ Q_i(x) => P_i(x) \}_{i=1}^{k}$$ all defined over $x \in \mathcal{X}$. I can use these rules and (automatically) ...
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112 views

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175 views

### Is Agda sound as a proof system? [closed]

I've asked the same question on CSSE but with no luck (https://cs.stackexchange.com/questions/89611/is-agda-sound-as-a-proof-system). Therefore I ask it again here in cstheory and hope that more ...
1answer
454 views

### Sparsification Lemma for k-SAT and Exponential Time Hypothesis

According to R. Impagliazzo, R. Paturi and F. Zane, 2001 an instance of $k$-SAT is called sparse if $m = O(n)$ where $m$ denotes the number of clauses and $n$ the number of variables. The ...
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88 views

### Looking for a specific tree automata model

is there any tree automata model over unranked trees (that is with unbounded number of children for each node), such that: Checking non-emptiness and universality is decidable in elementary time, ...
1answer
104 views

### Is Eulerian Path (or Eulerian Cycle) definable in Monadic Second Order Logic?

Does there exist a monadic second order logic formula which is satisfied by a graph if and only if it has an Eulerian path (or Eulerian cycle). I am looking for properties of graphs which are ...
0answers
219 views

### Fischer and Rabin's theorem (1974) for theories of “additive” structures

Fischer and Rabin's Super-Exponential Complexity of Presburger Arithmetic (1974) has the following theorem. (Theorem 12) Let $U$ be any class of additive structures, so if $A = (A, +) \in U$, ...
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41 views

### Is there a complete and finite axiom scheme for conditional independence? (Graphoids)

Note: This is a better-written version of an unanswered question asked before on MathOverflow. Question: Is there a complete and finite axiom scheme for conditional probability? If so, is ...
1answer
114 views

### Connection between algebraic logic and computational complexity of logics?

I'm learning a bit about algebraic logic and I was wondering how knowing the algebraic semantics of a given logic might help the study of the logic itself from a computational point of view. In ...
1answer
386 views

### Complexity of modal logic IK5

What is the complexity of local satisfiability problem for modal logic $\mathit{IK5}$? Herein we denote by $IK5$ the modal logic over euclidean frames extended with inverse modality. Could you provide ...